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W. and Luckhaus, S., Quasilinear elliptic-parabolic differential equations, Math. Z., 183, 1983, 311–341.\nAlt, H. W., Luckhaus, S. and Visintin, A., On nonstationary flow through porous media, Ann. Mat. Pura Appl., 136, 1984, 303–316.\nBernardi, C., El Alaoui, L. and Mghazli, Z., A posteriori analysis of a space and time discretization of a nonlinear model for the flow in variably saturated porous media, submitted.\nBerninger, H., Domain decomposition methods for elliptic problems with jumping nonlinearities and application to the Richards equation, Ph. D. Thesis, Freie Universität, Berlin, Germany, 2007.\nBrezzi, F., Hager, W. W. and Raviart, P. A., Error estimates for the finite element solution to variational inequalities. II. Mixed methods, Numer. Math., 31, 1978\u002F1979, 1–16.\nFabrié, P. and Gallouët, T., Modelling wells in porous media flows, Math. Models Methods Appl. Sci., 10, 2000, 673–709.\nGabbouhy, M., Analyse mathématique et simulation numérique des phénom`enes d’écoulement et de transport en milieux poreux non saturés. Application `a la région du Gharb, Ph. D. Thesis, University Ibn Tofail, Kénitra, Morocco, 2000.\nGirault, V. and Raviart, P. A., Finite Element Approximation of the Navier-Stokes Equations, Lecture Notes in Mathematics, 749, Springer-Verlag, Berlin, New York, 1979.\nGirault, V. and Raviart, P. A., Finite Element Methods for Navier-Stokes Equations, Theory and Algorithms, Springer-Verlag, Berlin, 1986.\nGlowinski, R., Lions, J. L. and Trémolières, R., Analyse numérique des inéquations variationnelles. 2. Applications aux phénom`enes stationnaires et d’évolution, Collection “Méthodes Mathématiques de l’Informatique” 5, Dunod, Paris, 1976.\nLions, J. L. and Magenes, E., Problèmes aux limites non homogènes et applications, Vol. I, Dunod, Paris, 1968.\nNochetto, R. H. and Verdi, C., Approximation of degenerate parabolic problems using numerical integration, SIAM J. Numer. Anal., 25, 1988, 784–814.\nRadu, F., Pop, I. S. and Knabner, P., Order of convergence estimates for an Euler implicit, mixed finite element discretization of Richards’ equation, SIAM J. Numer. Anal., 42, 2004, 1452–1478.\nRajagopal, K. R., On a hierarchy of approximate models for flows of incompressible fluids through porous solid, Math. Models Methods Appl. Sci., 17, 2007, 215–252.\nRichards, L. A., Capillary conduction of liquids through porous mediums, Physics, 1, 1931, 318–333.\nSchneid, E., Knabner, P. and Radu, F., A priori error estimates for a mixed finite element discretization of the Richards’ equation, Numer. Math., 98, 2004, 353–370.\nSochala, P. and Ern, A., Numerical methods for subsurface flows and coupling with runoff, to appear.\nSochala, P., Ern, A. and Piperno, S., Mass conservative BDF-discontinuous Galerkin\u002Fexplicit finite volume schemes for coupling subsurface and overland flows, Comput. Methods Appl. Mech. Engrg., 198, 2009, 2122–2136.\nWoodward, C. S. and Dawson, C. N., Analysis of expanded mixed finite element methods for a nonlinear parabolic equation modeling flow into variably saturated porous media, SIAM J. Numer. Anal., 37, 2000, 701–724.",{"EN":186},"The Richards equation models the water flow in a partially saturated underground porous medium under the surface. When it rains on the surface, boundary conditions of Signorini type must be considered on this part of the boundary. The authors first study this problem which results into a variational inequality and then propose a discretization by an implicit Euler’s scheme in time and finite elements in space. The convergence of this discretization leads to the well-posedness of the problem.",{"EN":188},"The rain on underground porous media Part I: Analysis of a richards model",{"VOID":190},"10.1007\u002Fs11401-013-0766-z","PUBLICATION","http:\u002F\u002Flink.springer.com\u002F10.1007\u002Fs11401-013-0766-z",[194,210,225],{"id":195,"sortIndex":121,"researcher":20,"roles":196,"affiliations":198,"properties":207},"ca5f8d99-6c15-4521-9fab-8bda7550ade7",[197],"AUTHOR",[199],{"id":20,"sortIndex":21,"affiliation":200,"properties":20},{"id":201,"createTime":202,"updateTime":202,"relativeEntities":203,"slug":20,"properties":204,"entityType":49,"verifyStatus":19,"verifyTime":20,"verifyNote":20,"syncStatus":19,"languages":20,"translateLanguages":20,"viewCount":21},"111d01cb-f3a3-479d-aad3-8e35ab22d79b","2023-12-07T23:53:49.323+00:00",[],{"title":205},{"VI":206},"Laboratoire de Mathématiques Raphaël Salem (UMR 6085 CNRS), Université de Rouen, Saint-Étienne-du-Rouvray, 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P. and Mellouk, M., On a stochastic partial differential equation with non-local diffusion, Potential Anal., 27(2), 2007 183–197.\nBo, L. J., Jiang, Y. M. and Wang, Y. J., On a class of stochastic Anderson models with fractional noises, Stoch. Anal. Appl., 26(2), 2008, 256–273.\nBo, L. J., Shi, K. H. and Wang, Y. J., On a nonlocal stochastic Kuramoto-Sivashinsky equation with jumps, Stoch. Dyn., 7(4), 2007, 439–457.\nBo, L. J., Jiang, Y. M. and Wang, Y. J., Stochastic Cahn-Hilliard equation with fractional noise, Stoch. Dyn., 8(4), 2008, 643–665.\nBo, L. J. and Wang, Y. J., Stochatic Cahn-Hilliard partial differential equations with Lévy spacetime noises, Stoch. Dyn., 6(2), 2006, 229–244.\nCardon-Weber, C., Cahn-Hilliard stochastic equation: existence of the solution and of its density, Bernoulli, 7(5), 2001, 777–816.\nDasgupta, A. and Kallianpur, G., Chaos decomposition of multiple fractional integrals and applications, Prob. Theory Relat. Fields, 115(4), 1999, 527–548.\nDebbi, L. and Dozzi, M., On the solutions of nonlinear stochastic fractional partial differential equations in one spatial dimension, Stoch. Proc. Appl., 115(11), 2005, 1764–1781.\nEidelman, S. D. and Zhitarashu, N. V., Parabolic Boundary Value Problems, Birkhäuser, Basel, 1998.\nHu, Y. Z., Heat equations with fractional white noise potentials, Appl. Math. Optim., 43(3), 2001, 221–243.\nHu, Y. Z., Chaos expansion of heat equations with white noise potentials, Potential Anal., 16(1), 2002, 45–66.\nJiang, Y. M., Shi, K. H. and Wang, Y. J., On a class of stochastic fractional partial differential equations with fractional noises, preprint, 2008.\nLe Mehaute, A., Machado, T., Trigeassou, J. C. and Sabatier, J., Fractional Differentiation and Its Applications, Proceedings of the First IFAC Workshop, Vol. 2004-1, International Federation of Automatic Control, ENSEIRB, Bordeaux, France, 2004.\nMann, J. A. and Woyczynski, W. A., Growing fractal interfaces in the presence of self-similar hopping surface diffusion, Phys. A, 291(1–4), 2001, 159–183.\nMémin, J., Mishura, Y. and Valkeila, E., Inequalities for moments of Wiener integrals with respect to a fractional Brownian motion, Stat. Prob. Lett., 51(2), 2001, 197–206.\nMetzler, R. and Klafter, J., The random walk’s guide to anomalous diffusion: a fractionl dynamics approach, Phys. Rep., 339, 2000, 1–77.\nMueller, C., Long-time existence for the heat equation with a noise term, Prob. Theory Relat. Fields, 90(4), 1991, 505–517.\nMueller, C. and Tribe, R., A measure-valued process related to the parabolic Anderson model, Prog. Prob., 52, 2002, 219–227.\nNualart, D. and Ouknine, Y., Regularization of quasilinear heat equations by a fractional noise, Stoch. Dyn., 4(2), 2004, 201–221.\nNualart, D. and Rozovskii, B., Weighted stochastic Sobolev spaces and bilinear SPDEs driven by spacetime white noise, J. Funct. Anal., 149(1), 1997, 200–225.\nNualart, D. and Zakai, M., Generalized Brownian functionals and the solution to a stochastic partial differential equation, J. Funct. Anal., 84(2), 1989, 279–296.\nNualart, D., Stochastic calculus with respect to the fractional Brownian motion and applications, Cont. Math., 336, 2003, 3–39.\nNualart, D., The Malliavin Calculus and Related Topics, Springer-Verlag, Heidelberg, 2006.\nPodlubny, I., Fractional Differential Equations, Academic Press, San Diego, 1999.\nUemura, H., Construction of the solution of 1-dimensional heat equation with white noise potential and its asymptotic behavior, Stoch. Anal. Appl., 14(4), 1996, 487–506.\nWalsh, J., An introduction to stochastic partial differential equations, Ecole d’Eté de Probabilité de Saint Fleur XIV, Lecture Notes in Math., 1180, Springer-Verlag, Berlin, 1986, 265–439.\nZaslavsky, G. M., Fractional kinetic equations for Hamiltonian chaos, Phys. D, 76(1–3), 1994, 110–122.\nZaslavsky, G. M. and Abdullaev, S. S., Scaling properties and anomalous transport of particles inside the stochastic layer, Phys. Rev. E, 51(5), 1995, 3901–3910.\nZhang, T. and Zheng, W., SPDEs driven by space-time white noises in high dimensions: absolute continuity of the law and convergence of solutions, Stoch. Stoch. Rep., 75(3), 2003, 103–128.",{"EN":289},"The authors are concerned with a class of one-dimensional stochastic Anderson models with double-parameter fractional noises, whose differential operators are fractional. A unique solution for the model in some appropriate Hilbert space is constructed. Moreover, the Lyapunov exponent of the solution is estimated, and its Hölder continuity is studied. On the other hand, the absolute continuity of the solution is also discussed.",{"EN":291},"Stochastic fractional Anderson models with fractional noises",{"VOID":293},"10.1007\u002Fs11401-008-0244-1","VERIFIED","Auto Verify","https:\u002F\u002Flink.springer.com\u002Farticle\u002F10.1007\u002Fs11401-008-0244-1",[298,313,325],{"id":299,"sortIndex":121,"researcher":20,"roles":300,"affiliations":301,"properties":310},"299727d2-097d-4d8c-acb2-2587640f670d",[197],[302],{"id":20,"sortIndex":21,"affiliation":303,"properties":20},{"id":304,"createTime":305,"updateTime":305,"relativeEntities":306,"slug":20,"properties":307,"entityType":49,"verifyStatus":19,"verifyTime":20,"verifyNote":20,"syncStatus":19,"languages":20,"translateLanguages":20,"viewCount":21},"51c21a28-0c78-4b45-878c-8be3be5ffdf8","2023-12-28T21:43:23.339+00:00",[],{"title":308},{"VI":309},"School of Mathematical Sciences and LPMC, Nankai University, Tianjin, China",{"title":311},{"VI":312},"Kehua 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T. and de Figueiredo, D. G., Infinitely many solutions of nonlinear elliptic systems, Prog. Nonlinear Diff. Eqs. Appl., 35, 1999, 51–67.\nBartsch, T. and Willem, M., Infinitely many non-radial solutions of a Euclidean scalar field equation, J. Funct. Anal., 117, 1993, 447–460.\nChang, K. C., Variational methods for non-differentiable functionals and their applications to partial differential equations, J. Math. Anal. Appl., 80, 1981, 102–129.\nClarke, F. H., Nonsmooth Analysis and Optimization, Wiley, New York, 1983.\nCosta, D. G., On a class of elliptic systems in R N, Electron, J. Diff. Eqs., 111, 1994, 103–122.\nde Figueiredo, D. G., Semilinear elliptic systems, Nonlinear Functional Analysis and Applications to Differential Equations, Trieste, 1997, World Science Publ., River Edge, New Jersey, 1998, 122–152.\nKrawcewicz, W. and Marzantowicz, W., Some remarks on the Lusternik-Schnirelman method for non-differentiable functionals invariant with respect to a finite group action, Rocky Mountain J. Math., 20, 1990, 1041–1049.\nKristály, A., Existence of nonzero weak solutions for a class of elliptic variational inclusions systems in R N, Nonlinear Anal., 65, 2006, 1578–1594.\nKristály, A., Exinstemce of two non-trivial solutions for a class of quasilinear elliptic variational systems on strip-like domains, Proc. Edinburgh Math. Soc., 48, 2005, 1–13.\nKristály, A., Lisei, H. and Varga, C., Multiple solutions for p-Laplacian type equations, Nonlinear Anal., 68, 2008, 1375–1381.\nKristály, A., Varga, C. and Varga, V., An eigenvalue problem for hemivariational inequalities with combined nonlinearities on an infinite strip, Nonlinear Anal., 63, 2005, 260–272.\nKristály, A., Varga, C. and Varga, V., A nonsmooth principle of symmetric criticality and variational-hemivariational inequalities, J. Math. Anal. Appl., 325, 2007, 975–986.\nMotreanu, D. and Panagiotopoulos, P. D., Minimax Theorems and Qualitative Properties of the Solutions of Hemivariational Inequalities, Kluwer Academic Publishers, Dordrecht, Boston, London, 1999.\nVelin, J., Existence results for some nonlinear elliptic system with lack of compactness, Nonlinear Anal., 52, 2002, 1017–1037.\nWillem, M., Minimax Theorems, Birkhäuser, Boston, 1996.\nYang, M. B. and Shen, Z. F., Multiplicity result for quasilinear elliptic systems with Neumann boundary condition, Acta Anal. Funct. Appl., 7(2), 2005, 146–150.",{"EN":383},"The authors study the existence of nontrivial solutions to p-Laplacian variational inclusion systems \n                  \n                    \n                  \n                  $\\left\\{ \\begin{gathered}\n   - \\Delta _p u + \\left| u \\right|^{p - 2} u \\in \\partial _1 F\\left( {u,v} \\right),  in \\mathbb{R}^N , \\hfill \\\\\n   - \\Delta _p v + \\left| v \\right|^{p - 2} v \\in \\partial _2 F\\left( {u,v} \\right),  in \\mathbb{R}^N , \\hfill \\\\\n\\end{gathered}  \\right.$\n                 where N ≥ 2, 2 ≤ p ≤ N and F: ℝ2 → ℝ is a locally Lipschitz function. Under some growth conditions on F, and by Mountain Pass Theorem and the principle of symmetric criticality, the existence of such solutions is guaranteed.",{"EN":385},"Existence of nontrivial solutions for p-Laplacian variational inclusion systems in ℝ N",{"VOID":387},"10.1007\u002Fs11401-011-0651-6","https:\u002F\u002Flink.springer.com\u002Farticle\u002F10.1007\u002Fs11401-011-0651-6",[390,405],{"id":391,"sortIndex":121,"researcher":20,"roles":392,"affiliations":393,"properties":402},"b031129e-a46b-49b0-af4f-dee156343927",[197],[394],{"id":20,"sortIndex":21,"affiliation":395,"properties":20},{"id":396,"createTime":397,"updateTime":397,"relativeEntities":398,"slug":20,"properties":399,"entityType":49,"verifyStatus":19,"verifyTime":20,"verifyNote":20,"syncStatus":19,"languages":20,"translateLanguages":20,"viewCount":21},"8de164e7-9561-499e-aa31-c85b77a2348b","2024-01-26T14:40:34.358+00:00",[],{"title":400},{"VI":401},"Department of Mathematics, Zhejiang Normal University, Jinhua, Zhejiang, China",{"title":403},{"VI":404},"Songqiang Wan",{"id":406,"sortIndex":21,"researcher":20,"roles":407,"affiliations":408,"properties":414},"94b2e6ac-f594-42ff-86a6-f2b59a2df982",[197],[409],{"id":20,"sortIndex":21,"affiliation":410,"properties":20},{"id":396,"createTime":397,"updateTime":397,"relativeEntities":411,"slug":20,"properties":412,"entityType":49,"verifyStatus":19,"verifyTime":20,"verifyNote":20,"syncStatus":19,"languages":20,"translateLanguages":20,"viewCount":21},[],{"title":413},{"VI":401},{"title":415},{"VI":416},"Zifei Shen",{"url":388,"publisher":418,"properties":446},{"id":6,"createTime":7,"updateTime":8,"relativeEntities":419,"slug":10,"properties":420,"entityType":18,"verifyStatus":19,"verifyTime":20,"verifyNote":20,"syncStatus":19,"languages":20,"translateLanguages":20,"viewCount":21,"subjectFields":424,"manageAffiliations":425,"indexDatabases":426,"url":104,"thumbnailPath":20,"statistic":441,"gsStatistic":20,"type":173,"analyzePriority":20},[],{"issn":421,"eissn":422,"title":423},{"VOID":13},{"VOID":15},{"EN":17},[],[],[427,434],{"id":86,"indexDatabase":428,"url":101,"indexYears":20,"academicFieldIds":433,"indexDatabaseRanking":20},{"id":88,"createTime":89,"updateTime":90,"relativeEntities":429,"label":430,"description":431,"key":97,"publicationTags":432,"standard":20},[],{"EN":93,"VI":93},{"VI":95,"EN":96},[99,100],[103],{"id":66,"indexDatabase":435,"url":79,"indexYears":80,"academicFieldIds":440,"indexDatabaseRanking":84},{"id":68,"createTime":69,"updateTime":70,"relativeEntities":436,"label":437,"description":438,"key":76,"publicationTags":439,"standard":20},[],{"EN":73,"VI":73},{"EN":73,"VI":75},[78],[82,83],{"impactFactor":21,"impactFactorByYear":442,"i10Index":118,"i10IndexLast5Year":21,"totalPublication":119,"totalPublicationByYear":443,"totalCitation":140,"totalCitationByYear":444,"totalCitationPerPublication":154,"totalCitationPerPublicationByYear":445,"hindexLast5Year":172,"hindex":172},{"2012":107,"2013":108,"2014":109,"2015":110,"2016":111,"2017":112,"2018":113,"2019":114,"2020":110,"2021":115,"2022":116,"2023":117},{"1999":121,"2000":122,"2006":123,"2007":124,"2008":125,"2009":126,"2010":127,"2011":128,"2012":129,"2013":130,"2014":131,"2015":132,"2016":133,"2017":132,"2018":134,"2019":135,"2020":136,"2021":130,"2022":137,"2023":138,"2024":139},{"1999":142,"2006":137,"2007":143,"2008":144,"2009":145,"2010":146,"2011":125,"2012":147,"2013":148,"2014":138,"2015":149,"2016":139,"2017":150,"2018":151,"2019":152,"2020":153,"2021":50,"2022":152,"2023":122},{"1999":142,"2006":156,"2007":157,"2008":158,"2009":159,"2010":160,"2011":161,"2012":162,"2013":163,"2014":164,"2015":165,"2016":166,"2017":167,"2018":168,"2019":169,"2020":170,"2021":171,"2022":113,"2023":116},{"volume":447,"pages":449},{"VOID":448},"32",{"VOID":450},"619-630","2011-07-08",2011,{"id":454,"createTime":455,"updateTime":456,"relativeEntities":457,"slug":458,"properties":459,"entityType":191,"verifyStatus":294,"verifyTime":456,"verifyNote":295,"syncStatus":19,"languages":20,"translateLanguages":20,"viewCount":21,"primaryUrl":468,"fullTextUrl":20,"authors":469,"publicationType":241,"publisherRelationship":497,"citationCount":20,"citationInfo":20,"publishDate":531,"publishYear":532,"citationAnalyzeStatus":19,"lastCitationAnalyze":20,"indexDatabases":20,"openAccess":20,"references":20,"isForceReanalyzing":278},"40a283fc-e1bc-47b8-81ab-324d7b66236a","2024-01-09T13:47:27.168+00:00","2024-09-13T23:48:31.282+00:00",[],"Boundedness-and-Almost-Periodicity-of-Solutions-for-a-Class-of-Semilinear-Parabolic-Equations-with-Boundary-Degeneracy",{"references":460,"abstract":462,"title":464,"doi":466},{"VOID":461},"Amar, M. and Gianni, R., Almost-periodic solutions of elliptic and parabolic equations in unbounded domains, Proc. Roy. Soc. Edinburgh Sect. A, 132(6), 2002, 1275–1306.\nAsanova, A. T., A bounded almost periodic solution of a semilinear parabolic equation, Izv. Minister. Nauki Akad. Nauk Resp. Kaz. Ser. Fiz.-Mat., 5, 1996, 17–22 (in Russian).\nCai, J. J. and Lou, B. D., Convergence in a quasilinear parabolic equation with time almost periodic boundary conditions, Nonlinear Anal., 75, 2012, 6312–6324.\nCannarsa, P., Martinez, P. and Vancostenoble, J., Persistent regional null controllability for a class of degenerate parabolic equations, Commun. Pure Appl. Anal., 3(4), 2004, 607–635.\nCannarsa, P., Martinez, P. and Vancostenoble, J., Null controllability of degenerate heat equations, Adv. Differential Equations, 10(2), 2005, 153–190.\nCorduneanu, C., Almost Periodic Oscillations and Wave, Springer-Verlag, New York, 2009.\nDamlamian, A. and Kenmochi, N., Asymptotic behavior of solutions to a multiphase Stefan problem, Japan J. Appl. Math., 3, 1986, 15–36.\nDamlamian, A. and Kenmochi, N., Periodicity and almost periodicity of solutions to a multi-phase Stefan problem in several space variables, Nonlinear Anal., 12(9), 1988, 921–934.\nEvans, L. C., Partial Differential Equations, Graduate Studies in Mathematics, 19, Amer. Math. Soc. Providence, RI, 1998.\nKeldys, M. V., On certain cases of degeneration of equations of elliptic type on the boundary of a domain, Dokl. Akad. Nauk SSSR, 77, 1951, 181–183.\nKubo, M., Periodic and almost periodic stability of solutions to degenerate parabolic equations, Hiroshima Math. J., 19, 1989, 499–514.\nKufner, A., Weighted Sobolev Spaces, John Wiley & Sons, Chichester, New York, Brisbane, Toronto, Singapore, 1985.\nLevenshtam, V. B., On the unique solvability of parabolic equations with almost periodic coefficients in Holder spaces, Mat. Zametki, 73(6), 2003, 861–877 (in Russian).\nLevitan, B. M. and Zhikov, V. V., Almost Periodic Functions and Differential Equations, Combridge University Press, Combridge, 1982.\nNakao, M., On boundedness, periodicity, and almost periodicity of solutions of some nonlinear parabolic equations, J. Differential Equations, 19, 1975, 371–385.\nNakao, M. and Nanbu, T., On the existence of global, bounded, periodic and almost-periodic solutions of nonlinear parabolic equations, Math. Rep. Kyushu Univ., 10(2), 1975, 99–112.\nOleinik, O. A. and Radkevic, E. V., Second-Order Equations with Nonnegative Characteristic Forms, Amer. Math. Soc., Pleum Press, New York, 1973.\nRossi, L., Liouville type results for periodic and almost periodic linear operators, Ann. Inst. H. Poincaré Anal. Non Linéaire, 26(6), 2009, 2481–2502.\nShen, W. X. and Yi, Y. F., Asymptotic almost periodicity of scalar parabolic equations with almost periodic time dependence, J. Differential Equations, 122(2), 1995, 373–397.\nShen, W. X. and Yi, Y. F., Almost automorphic and almost periodic dynamics in skew-product semiflows, Mem. Amer. Math. Soc., 136 (647), 1998.\nVuillermot, P. A., Global exponential attractors for a class of almost-periodic parabolic equations in ℝN, Proc. Amer. Math. Soc., 116, 1992, 775–782.\nWang, C. P., Approximate controllability of a class of semilinear systems with boundary degeneracy, J. Evol. Equ., 10, 2010, 163–193.\nWard, J. R., Bounded and almost periodic solutions of semilinear parabolic equations, Rocky Mountain J. Math., 18, 1988, 479–494.\nYamazaki, N., Almost periodicity of solutions to free boundary problems, Dynamical Systems and Differential Equations (Kennesaw, GA, 2000), Discrete Contin. Dynam. Systems, Added Volume, 2001, 386–397.\nYin, J. X. and Wang, C. P., Evolutionary weighted p-Laplacian with boundary degeneracy, J. Differential Equations, 237(2), 2007, 421–445.",{"EN":463},"In this paper the authors investigate the boundedness and almost periodicity of solutions of semilinear parabolic equations with boundary degeneracy. The equations may be weakly degenerate or strongly degenerate on the lateral boundary. The authors prove the existence, uniqueness and global exponential stability of bounded entire solutions, and also establish the existence theorem of almost periodic solutions if the data are almost periodic.",{"EN":465},"Boundedness and Almost Periodicity of Solutions for a Class of Semilinear Parabolic Equations with Boundary Degeneracy",{"VOID":467},"10.1007\u002Fs11401-020-0200-2","https:\u002F\u002Flink.springer.com\u002Farticle\u002F10.1007\u002Fs11401-020-0200-2",[470,485],{"id":471,"sortIndex":21,"researcher":20,"roles":472,"affiliations":473,"properties":482},"e971fdfa-5baf-41bd-8ef8-6ae4b5f14866",[197],[474],{"id":20,"sortIndex":21,"affiliation":475,"properties":20},{"id":476,"createTime":477,"updateTime":477,"relativeEntities":478,"slug":20,"properties":479,"entityType":49,"verifyStatus":19,"verifyTime":20,"verifyNote":20,"syncStatus":19,"languages":20,"translateLanguages":20,"viewCount":21},"97115af9-0d0b-4c4e-adfa-3c0d4e90952f","2024-01-04T22:27:16.157+00:00",[],{"title":480},{"VI":481},"School of Mathematical Sciences, South China Normal University, Guangzhou, China",{"title":483},{"VI":484},"Yi Xie",{"id":486,"sortIndex":121,"researcher":20,"roles":487,"affiliations":488,"properties":494},"e0383b6c-ca5c-4a81-97d5-7105108b0a6f",[197],[489],{"id":20,"sortIndex":21,"affiliation":490,"properties":20},{"id":476,"createTime":477,"updateTime":477,"relativeEntities":491,"slug":20,"properties":492,"entityType":49,"verifyStatus":19,"verifyTime":20,"verifyNote":20,"syncStatus":19,"languages":20,"translateLanguages":20,"viewCount":21},[],{"title":493},{"VI":481},{"title":495},{"VI":496},"Peidong Lei",{"url":468,"publisher":498,"properties":526},{"id":6,"createTime":7,"updateTime":8,"relativeEntities":499,"slug":10,"properties":500,"entityType":18,"verifyStatus":19,"verifyTime":20,"verifyNote":20,"syncStatus":19,"languages":20,"translateLanguages":20,"viewCount":21,"subjectFields":504,"manageAffiliations":505,"indexDatabases":506,"url":104,"thumbnailPath":20,"statistic":521,"gsStatistic":20,"type":173,"analyzePriority":20},[],{"issn":501,"eissn":502,"title":503},{"VOID":13},{"VOID":15},{"EN":17},[],[],[507,514],{"id":86,"indexDatabase":508,"url":101,"indexYears":20,"academicFieldIds":513,"indexDatabaseRanking":20},{"id":88,"createTime":89,"updateTime":90,"relativeEntities":509,"label":510,"description":511,"key":97,"publicationTags":512,"standard":20},[],{"EN":93,"VI":93},{"VI":95,"EN":96},[99,100],[103],{"id":66,"indexDatabase":515,"url":79,"indexYears":80,"academicFieldIds":520,"indexDatabaseRanking":84},{"id":68,"createTime":69,"updateTime":70,"relativeEntities":516,"label":517,"description":518,"key":76,"publicationTags":519,"standard":20},[],{"EN":73,"VI":73},{"EN":73,"VI":75},[78],[82,83],{"impactFactor":21,"impactFactorByYear":522,"i10Index":118,"i10IndexLast5Year":21,"totalPublication":119,"totalPublicationByYear":523,"totalCitation":140,"totalCitationByYear":524,"totalCitationPerPublication":154,"totalCitationPerPublicationByYear":525,"hindexLast5Year":172,"hindex":172},{"2012":107,"2013":108,"2014":109,"2015":110,"2016":111,"2017":112,"2018":113,"2019":114,"2020":110,"2021":115,"2022":116,"2023":117},{"1999":121,"2000":122,"2006":123,"2007":124,"2008":125,"2009":126,"2010":127,"2011":128,"2012":129,"2013":130,"2014":131,"2015":132,"2016":133,"2017":132,"2018":134,"2019":135,"2020":136,"2021":130,"2022":137,"2023":138,"2024":139},{"1999":142,"2006":137,"2007":143,"2008":144,"2009":145,"2010":146,"2011":125,"2012":147,"2013":148,"2014":138,"2015":149,"2016":139,"2017":150,"2018":151,"2019":152,"2020":153,"2021":50,"2022":152,"2023":122},{"1999":142,"2006":156,"2007":157,"2008":158,"2009":159,"2010":160,"2011":161,"2012":162,"2013":163,"2014":164,"2015":165,"2016":166,"2017":167,"2018":168,"2019":169,"2020":170,"2021":171,"2022":113,"2023":116},{"volume":527,"pages":529},{"VOID":528},"41",{"VOID":530},"303-324","2020-04-03",2020,{"id":534,"createTime":535,"updateTime":536,"relativeEntities":537,"slug":538,"properties":539,"entityType":191,"verifyStatus":294,"verifyTime":536,"verifyNote":295,"syncStatus":19,"languages":20,"translateLanguages":20,"viewCount":21,"primaryUrl":548,"fullTextUrl":20,"authors":549,"publicationType":241,"publisherRelationship":583,"citationCount":20,"citationInfo":20,"publishDate":617,"publishYear":618,"citationAnalyzeStatus":19,"lastCitationAnalyze":20,"indexDatabases":20,"openAccess":20,"references":20,"isForceReanalyzing":278},"e8d60a70-3f1b-489d-8358-96f55631419e","2024-01-30T20:15:35.531+00:00","2024-12-05T23:48:13.489+00:00",[],"Asymptotic-results-for-tail-probabilities-of-sums-of-dependent-and-heavy-tailed-random-variables",{"references":540,"abstract":542,"title":544,"doi":546},{"VOID":541},"Albrecher, H., Asmussen, S. and Kortschak, D., Tail asymptotics for the sum of two heavy-tailed dependent risks, Extremes, 9, 2006, 107–130.\nAsmussen, S., Ruin Probabilities, World Scientific, Singapore, 2000.\nBingham, N. H., Goldie, C. M. and Teugels, J. L., Regular Variation, Cambridge University Press, Cambridge, 1987.\nChen, Y. and Yuen, K. C., Sums of pairwise quasi-asymptotically independent random variables with consistent variation, Stoch. Models, 25, 2009, 76–89.\nDenisov, D., Foss, S. and Korshunov, D., Tail asymptotics for the supremum of a random walk when the mean is not finite, Queueing Syst., 46, 2004, 15–33.\nDenisov, D., Foss, S. and Korshunov, D., On lower limits and equivalences for distribution tails of randomly stopped sums, Bernoulli, 14, 2008, 391–404.\nDenisov, D., Foss, S. and Korshunov, D., Lower limits for distribution tails of randomly stopped sums, Theory Probab. Appl., 52, 2008, 690–699.\nDenisov, D., Foss, S. and Korshunov, D., Asymptotics of randomly stopped sums in the presence of heavy tails, Bernoulli, 16(4), 2010, 971–994.\nEmbrechts, P., Goldie, C. M. and Veraverbeke, N., Subexponentiality and infinite divisibility, Z. Wahrsch. Verw. Gebiete, 49, 1979, 335–347.\nEmbrechts, P., Klüppelberg, C. and Mikosch, T., Modelling Extremal Events for Insurance and Finance, Springer-Verlag, Berlin, 1997.\nFoss, S. and Korshunov, D., Lower limits and equivalences for convolution tails, Ann. Probab., 35, 2007, 366–383.\nFoss, S. and Richards, A., On sums of conditionally independent subexponential random variables, Math. Oper. Res., 35(1), 2010, 102–119.\nGeluk, J. and Tang, Q. H., Asymptotic tail probabilities of sums of dependent subexponential random variables, J. Theoret. Probab., 22, 2009, 871–882.\nKaas, R. and Tang, Q. H., Note on the tail behavior of random walk maxima with heavy tails and negative drift, North Amer. Actuar. J., 7(3), 2003, 57–61.\nKlüppelberg, C., Subexponential distributions and integrated tails, J. Appl. Probab., 25, 1988, 132–141.\nKo, B. and Tang, Q. H., Sums of dependent nonnegative random variables with subexponential tails, J. Appl. Probab., 45, 2008, 85–95.\nKorshunov, D., Large-deviation probabilities for maxima of sums of independent random variables with negative mean and subexponential distribution, Theory Probab. Appl., 46, 2002, 355–366.\nKotz, S., Balakrishnan, N. and Johnson, N. L., Continuous Multivariate Distributions: Models and Applications, 2nd ed., Vol. 1, Wiley, New York, 2000.\nNelsen, R. B., An Introduction to Copulas, 2nd ed., Springer-Verlag, New York, 2006.\nNg, K. W., Tang, Q. H., Yan, J. A. and Yang, H. L., Precise large deviations for the prospective-loss process, J. Appl. Probab., 40, 2003, 391–400.\nNg, K. W. and Tang, Q. H., Asymptotic behavior of tail and local probabilities for sums of subexponential random variables, J. Appl. Probab., 41, 2004, 108–116.\nNg, K. W., Tang, Q. H. and Yang, H. L., Maxima of sums of heavy-tailed random variables, ASTIN Bull., 32, 2002, 43–55.\nResnick, S. I., Hidden regular variation, second order regular variation and asymptotic independence, Extremes, 5, 2002, 303–336.\nTang, Q. H., The ruin probability of a discrete time risk model under constant interest rate with heavy tails, Scandinavian Actuarial Journal, 3, 2004, 229–240.\nTang, Q. H., Asymptotic ruin probabilities in finite horizon with subexponential losses and associated discount factors, Probab. Engrg. Inform. Sci., 20, 2006, 103–113.\nYu, C., Wang, Y. and Cui, Z., Lower limits and upper limits for tails of random sums supported on ℝ, Statist. Prob. Lett., 80, 2010, 1111–1120.",{"EN":543},"Let X\n                1,X\n                2, ... be a sequence of dependent and heavy-tailed random variables with distributions F\n                1, F\n                2, ... on (−∞,∞), and let τ be a nonnegative integer-valued random variable independent of the sequence {X\n                \n                  k\n                , k ≥ 1}. In this framework, the asymptotic behavior of the tail probabilities of the quantities \n                  \n                    \n                  \n                  $$S_n  = \\sum\\limits_{k = 1}^n {X_k }$$\n                 and \n                  \n                    \n                  \n                  $$S_{(n)}  = \\mathop {\\max }\\limits_{1 \\leqslant k \\leqslant n} S_k$$\n                 for n > 1, and their randomized versions S\n                \n                  τ\n                 and S\n                (τ) are studied. Some applications to the risk theory are presented.",{"EN":545},"Asymptotic results for tail probabilities of sums of dependent and heavy-tailed random variables",{"VOID":547},"10.1007\u002Fs11401-012-0723-2","https:\u002F\u002Flink.springer.com\u002Farticle\u002F10.1007\u002Fs11401-012-0723-2",[550,566],{"id":551,"sortIndex":121,"researcher":20,"roles":552,"affiliations":553,"properties":563},"f528e65c-4fb1-4f28-b695-1a8f6be655b8",[197],[554],{"id":20,"sortIndex":21,"affiliation":555,"properties":20},{"id":556,"createTime":557,"updateTime":557,"relativeEntities":558,"slug":559,"properties":560,"entityType":49,"verifyStatus":19,"verifyTime":20,"verifyNote":20,"syncStatus":19,"languages":20,"translateLanguages":20,"viewCount":21},"a99d5440-a6dd-4e76-9d5d-d698306db927","2024-04-19T03:59:12.829+00:00",[],"School-of-Mathematical-Sciences-Qufu-Normal-University-Qufu-Shandong-China",{"title":561},{"EN":562},"School of Mathematical Sciences, Qufu Normal University, Qufu, Shandong, China",{"title":564},{"VI":565},"Chuancun Yin",{"id":567,"sortIndex":21,"researcher":20,"roles":568,"affiliations":569,"properties":580},"29ca3d3d-3725-4ee8-8e7f-27ee7786ddc2",[197],[570],{"id":20,"sortIndex":21,"affiliation":571,"properties":20},{"id":572,"createTime":573,"updateTime":574,"relativeEntities":575,"slug":576,"properties":577,"entityType":49,"verifyStatus":19,"verifyTime":20,"verifyNote":20,"syncStatus":19,"languages":20,"translateLanguages":20,"viewCount":21},"ee77da87-3c2b-40d3-8412-032797ea0d06","2024-04-18T23:39:29.757+00:00","2024-10-06T23:33:07.057+00:00",[],"Department-of-Statistics-and-Actuarial-Science-The-University-of-Hong-Kong-Hong-Kong-China",{"title":578},{"EN":579},"Department of Statistics and Actuarial Science, The University of Hong Kong, Hong Kong, China",{"title":581},{"VI":582},"Kam Chuen Yuen",{"url":548,"publisher":584,"properties":612},{"id":6,"createTime":7,"updateTime":8,"relativeEntities":585,"slug":10,"properties":586,"entityType":18,"verifyStatus":19,"verifyTime":20,"verifyNote":20,"syncStatus":19,"languages":20,"translateLanguages":20,"viewCount":21,"subjectFields":590,"manageAffiliations":591,"indexDatabases":592,"url":104,"thumbnailPath":20,"statistic":607,"gsStatistic":20,"type":173,"analyzePriority":20},[],{"issn":587,"eissn":588,"title":589},{"VOID":13},{"VOID":15},{"EN":17},[],[],[593,600],{"id":86,"indexDatabase":594,"url":101,"indexYears":20,"academicFieldIds":599,"indexDatabaseRanking":20},{"id":88,"createTime":89,"updateTime":90,"relativeEntities":595,"label":596,"description":597,"key":97,"publicationTags":598,"standard":20},[],{"EN":93,"VI":93},{"VI":95,"EN":96},[99,100],[103],{"id":66,"indexDatabase":601,"url":79,"indexYears":80,"academicFieldIds":606,"indexDatabaseRanking":84},{"id":68,"createTime":69,"updateTime":70,"relativeEntities":602,"label":603,"description":604,"key":76,"publicationTags":605,"standard":20},[],{"EN":73,"VI":73},{"EN":73,"VI":75},[78],[82,83],{"impactFactor":21,"impactFactorByYear":608,"i10Index":118,"i10IndexLast5Year":21,"totalPublication":119,"totalPublicationByYear":609,"totalCitation":140,"totalCitationByYear":610,"totalCitationPerPublication":154,"totalCitationPerPublicationByYear":611,"hindexLast5Year":172,"hindex":172},{"2012":107,"2013":108,"2014":109,"2015":110,"2016":111,"2017":112,"2018":113,"2019":114,"2020":110,"2021":115,"2022":116,"2023":117},{"1999":121,"2000":122,"2006":123,"2007":124,"2008":125,"2009":126,"2010":127,"2011":128,"2012":129,"2013":130,"2014":131,"2015":132,"2016":133,"2017":132,"2018":134,"2019":135,"2020":136,"2021":130,"2022":137,"2023":138,"2024":139},{"1999":142,"2006":137,"2007":143,"2008":144,"2009":145,"2010":146,"2011":125,"2012":147,"2013":148,"2014":138,"2015":149,"2016":139,"2017":150,"2018":151,"2019":152,"2020":153,"2021":50,"2022":152,"2023":122},{"1999":142,"2006":156,"2007":157,"2008":158,"2009":159,"2010":160,"2011":161,"2012":162,"2013":163,"2014":164,"2015":165,"2016":166,"2017":167,"2018":168,"2019":169,"2020":170,"2021":171,"2022":113,"2023":116},{"volume":613,"pages":615},{"VOID":614},"33",{"VOID":616},"557-568","2012-07-10",2012,{"id":620,"createTime":621,"updateTime":622,"relativeEntities":623,"slug":624,"properties":625,"entityType":191,"verifyStatus":294,"verifyTime":638,"verifyNote":295,"syncStatus":19,"languages":20,"translateLanguages":639,"viewCount":21,"primaryUrl":641,"fullTextUrl":20,"authors":642,"publicationType":241,"publisherRelationship":658,"citationCount":20,"citationInfo":20,"publishDate":692,"publishYear":693,"citationAnalyzeStatus":19,"lastCitationAnalyze":20,"indexDatabases":20,"openAccess":20,"references":20,"isForceReanalyzing":278},"3a120769-ccc6-44b7-a860-174b52806c01","2024-01-09T12:27:57.611+00:00","2025-02-10T23:46:14.478+00:00",[],"f-Harmonic-morphisms-between-Riemannian-manifolds",{"references":626,"abstract":628,"title":631,"doi":634,"keywords":636},{"VOID":627},"Ababou, R., Baird, P. and Brossard, J., Polynômes semi-conformes et morphismes harmoniques, Math. Z., 231(3), 1999, 589–604.\nAra, M., Geometry of F-harmonic maps, Kodai Math. J., 22(2), 1999, 243–263.\nBaird, P. and Gudmundsson, S., p-harmonic maps and minimal submanifolds, Math. Ann., 294, 1992, 611–624.\nBaird, P. and Wood, J. C., Harmonic morphisms between Riemannian manifolds, London Math. Soc. Monogr. New Series, 29, Oxford Univ. Press, Oxford, 2003.\nCieślński, J., Goldstein, P. and Sym, A., On integrability of the inhomogeneous Heisenberg ferromagnet model: Examination of a new test, J. Phys. A: Math. Gen., 27, 1994, 1645–1664.\nCieślński, J., Sym, A. and Wesselius, W., On the geometry of the inhomogeneous Heisenberg ferromagnet: Non-integrable case, J. Phys. A: Math. Gen., 26, 1993, 1353–1364.\nCourse, N., f-harmonic maps, Thesis, University of Warwick, Coventry, CV47AL, UK, 2004.\nCourse, N., f-Harmonic maps which map the boundary of the domain to one point in the target, New York J. Math, 13, 2007, 423–435.\nDaniel, M., Porsezian, K. and Lakshmanan, M., On the integrability of the inhomogeneous spherically symmetric Heisenberg ferromagnet in arbitrary dimension, J. Math. Phys., 35(10), 1994, 6498–6510.\nEells, J. and Lemaire, L., A report on harmonic maps, Bull. London Math. Soc., 10, 1978, 1–68.\nFuglede, B., Harmonic morphisms between Riemannian manifolds, Ann. Inst. Fourier (Grenoble), 28, 1978, 107–144.\nGudmundsson, S., The geometry of harmonic morphisms, Ph. D. Thesis, University of Leeds, UK, 1992.\nHeller, S., Harmonic morphisms on conformally flat 3-spheres, Bull. London Math. Soc., 43(1), 2011, 137–150.\nHuang, P. and Tang, H., On the heat flow of f-harmonic maps from D 2 into S 2, Nonlinear Anal., 67(7), 2007, 2149–2156.\nIshihara, T., A mapping of Riemannian manifolds which preserves harmonic functions, J. Math. Kyoto Univ., 19(2), 1979, 215–229.\nLakshmanan, M. and Bullough, R. K., Geometry of generalised nonlinear Schrödinger and Heisenberg ferromagnetic spin equations with x-dependent coefficients, Phys. Lett. A, 80(4), 1980, 287–292.\nLi, Y. X. and Wang, Y. D, Bubbling location for f-harmonic maps and inhomogeneous Landau-Lifshitz equations, Comment. Math. Helv., 81(2), 2006, 433–448.\nLichnerowicz, A., Applications harmoniques et variétés kähleriennes, Symposia Mathematica III, Academic Press, London, 1970, 341–402.\nLoubeau, E., On p-harmonic morphisms, Diff. Geom. and Its Appl., 12, 2000, 219–229.\nManfredi, J. and Vespri, V., n-harmonic morphisms in space are Möbius transformations, Michigan Math. J., 41, 1994, 135–142.\nOu, Y. -L., p-harmonic morphisms, minimal foliations, and rigidity of metrics, J. Geom. Phys., 52(4), 2004, 365–381.\nOu, Y. -L. and Wilhelm, F., Horizontally homothetic submersions and nonnegative curvature, Indiana Univ. Math. J., 56(1), 2007, 243–261.\nOuakkas, S., Nasri, R. and Djaa, M., On the f-harmonic and f-biharmonic maps, JP J. Geom. Topol., 10(1), 2010, 11–27.\nTakeuchi, H., Some conformal properties of p-harmonic maps and regularity for sphere-valued p-harmonic maps, J. Math. Soc. Japan, 46, 1994, 217–234.",{"EN":629,"VI":630},"\n                f-Harmonic maps were first introduced and studied by Lichnerowicz in 1970. In this paper, the author studies a subclass of f-harmonic maps called f-harmonic morphisms which pull back local harmonic functions to local f-harmonic functions. The author proves that a map between Riemannian manifolds is an f-harmonic morphism if and only if it is a horizontally weakly conformal f-harmonic map. This generalizes the well-known characterization for harmonic morphisms. Some properties and many examples as well as some non-existence of f-harmonic morphisms are given. The author also studies the f-harmonicity of conformal immersions.","\n                Các bản đồ f-Harmonic lần đầu tiên được giới thiệu và nghiên cứu bởi Lichnerowicz vào năm 1970. Trong bài báo này, tác giả nghiên cứu một phân lớp của các bản đồ f-harmonic gọi là các biến hình f-harmonic, có khả năng kéo ngược các hàm hài hòa địa phương thành các hàm f-harmonic địa phương. Tác giả chứng minh rằng một bản đồ giữa các đa tạp Riemann là một biến hình f-harmonic nếu và chỉ nếu nó là một bản đồ f-harmonic yếu đồng điều theo chiều ngang. Điều này tổng quát hóa đặc điểm nổi tiếng đối với các biến hình hài hòa. Một số tính chất và nhiều ví dụ cũng như một số trường hợp không tồn tại của các biến hình f-harmonic được đưa ra. Tác giả cũng nghiên cứu tính chất f-harmonicity của các sự nhúng đồng điều.",{"EN":632,"VI":633},"f-Harmonic morphisms between Riemannian manifolds","Biến hình f-Harmonic giữa các đa tạp Riemann",{"VOID":635},"10.1007\u002Fs11401-014-0825-0",{"VI":637},"f-harmonic, Riemannian manifold, morphism, harmonicity, conformal immersion","2025-02-05T17:54:13.890+00:00",[640],"VI","https:\u002F\u002Flink.springer.com\u002Farticle\u002F10.1007\u002Fs11401-014-0825-0",[643],{"id":644,"sortIndex":21,"researcher":20,"roles":645,"affiliations":646,"properties":655},"df999b02-db00-4d9e-84c1-d67eb0b0057e",[197],[647],{"id":20,"sortIndex":21,"affiliation":648,"properties":20},{"id":649,"createTime":650,"updateTime":650,"relativeEntities":651,"slug":20,"properties":652,"entityType":49,"verifyStatus":19,"verifyTime":20,"verifyNote":20,"syncStatus":19,"languages":20,"translateLanguages":20,"viewCount":21},"350ab45c-b5d3-432f-a6ae-38e21fae5428","2024-01-09T12:27:57.627+00:00",[],{"title":653},{"VI":654},"Department of Mathematics, Guangxi University for Nationalities, Nanning, China",{"title":656},{"VI":657},"Yelin Ou",{"url":641,"publisher":659,"properties":687},{"id":6,"createTime":7,"updateTime":8,"relativeEntities":660,"slug":10,"properties":661,"entityType":18,"verifyStatus":19,"verifyTime":20,"verifyNote":20,"syncStatus":19,"languages":20,"translateLanguages":20,"viewCount":21,"subjectFields":665,"manageAffiliations":666,"indexDatabases":667,"url":104,"thumbnailPath":20,"statistic":682,"gsStatistic":20,"type":173,"analyzePriority":20},[],{"issn":662,"eissn":663,"title":664},{"VOID":13},{"VOID":15},{"EN":17},[],[],[668,675],{"id":86,"indexDatabase":669,"url":101,"indexYears":20,"academicFieldIds":674,"indexDatabaseRanking":20},{"id":88,"createTime":89,"updateTime":90,"relativeEntities":670,"label":671,"description":672,"key":97,"publicationTags":673,"standard":20},[],{"EN":93,"VI":93},{"VI":95,"EN":96},[99,100],[103],{"id":66,"indexDatabase":676,"url":79,"indexYears":80,"academicFieldIds":681,"indexDatabaseRanking":84},{"id":68,"createTime":69,"updateTime":70,"relativeEntities":677,"label":678,"description":679,"key":76,"publicationTags":680,"standard":20},[],{"EN":73,"VI":73},{"EN":73,"VI":75},[78],[82,83],{"impactFactor":21,"impactFactorByYear":683,"i10Index":118,"i10IndexLast5Year":21,"totalPublication":119,"totalPublicationByYear":684,"totalCitation":140,"totalCitationByYear":685,"totalCitationPerPublication":154,"totalCitationPerPublicationByYear":686,"hindexLast5Year":172,"hindex":172},{"2012":107,"2013":108,"2014":109,"2015":110,"2016":111,"2017":112,"2018":113,"2019":114,"2020":110,"2021":115,"2022":116,"2023":117},{"1999":121,"2000":122,"2006":123,"2007":124,"2008":125,"2009":126,"2010":127,"2011":128,"2012":129,"2013":130,"2014":131,"2015":132,"2016":133,"2017":132,"2018":134,"2019":135,"2020":136,"2021":130,"2022":137,"2023":138,"2024":139},{"1999":142,"2006":137,"2007":143,"2008":144,"2009":145,"2010":146,"2011":125,"2012":147,"2013":148,"2014":138,"2015":149,"2016":139,"2017":150,"2018":151,"2019":152,"2020":153,"2021":50,"2022":152,"2023":122},{"1999":142,"2006":156,"2007":157,"2008":158,"2009":159,"2010":160,"2011":161,"2012":162,"2013":163,"2014":164,"2015":165,"2016":166,"2017":167,"2018":168,"2019":169,"2020":170,"2021":171,"2022":113,"2023":116},{"volume":688,"pages":690},{"VOID":689},"35",{"VOID":691},"225-236","2014-03-06",2014,{"id":695,"createTime":696,"updateTime":697,"relativeEntities":698,"slug":699,"properties":700,"entityType":191,"verifyStatus":294,"verifyTime":697,"verifyNote":295,"syncStatus":19,"languages":20,"translateLanguages":20,"viewCount":21,"primaryUrl":709,"fullTextUrl":710,"authors":711,"publicationType":241,"publisherRelationship":774,"citationCount":20,"citationInfo":20,"publishDate":809,"publishYear":532,"citationAnalyzeStatus":19,"lastCitationAnalyze":20,"indexDatabases":20,"openAccess":20,"references":20,"isForceReanalyzing":278},"33e8b195-59ea-4cc3-8358-51699ac75187","2023-12-08T14:21:55.437+00:00","2024-12-05T23:46:08.138+00:00",[],"Structural-Properties-of-Homomorphism-Dilation-Systems",{"references":701,"abstract":703,"title":705,"doi":707},{"VOID":702},"citation_title=Dilation theory yesterday and today, A Glimpse at Hilbert Space Operators; citation_inbook_title=Oper. Theory Adv. Appl.; citation_publication_date=2010; citation_pages=99-123; citation_id=CR1; citation_author=W Arveson; citation_publisher=Birkhauser Verlag\ncitation_journal_title=Contemp. Math.; citation_title=Frames for Banach spaces, The Functional and Harmonic Analysis of Wavelets and Frames (San Antonio, TX, 1999); citation_author=P G Casazza, D G Han, D R Larson; citation_volume=247; citation_publication_date=1999; citation_pages=149-182; citation_doi=10.1090\u002Fconm\u002F247\u002F03801; citation_id=CR2\ncitation_journal_title=Adv. Comput. Math.; citation_title=Frames associated with measurable spaces; citation_author=J P Gabardo, D G Han; citation_volume=18; citation_publication_date=2003; citation_pages=127-147; citation_doi=10.1023\u002FA:1021312429186; citation_id=CR3\ncitation_journal_title=J. Operator Theory; citation_title=Frame representations for group-like unitary operator systems; citation_author=J P Gabardo, D G Han; citation_volume=49; citation_publication_date=2003; citation_pages=223-244; citation_id=CR4\ncitation_journal_title=Canad. J. Math.; citation_title=Dilations and Hahn decompositions for linear maps; citation_author=D W Hadwin; citation_volume=33; citation_publication_date=1981; citation_pages=826-839; citation_doi=10.4153\u002FCJM-1981-064-7; citation_id=CR5\ncitation_journal_title=J. Fourier Anal. Appl.; citation_title=Dilations and completions for Gabor systems; citation_author=D G Han; citation_volume=15; citation_publication_date=2009; citation_pages=201-217; citation_doi=10.1007\u002Fs00041-008-9028-y; citation_id=CR6\ncitation_journal_title=Mem. Amer. Math. Soc.; citation_title=Frames, bases and group representations; citation_author=D G Han, D R Larson; citation_volume=697; citation_publication_date=2000; citation_pages=1-94; citation_id=CR7\nHan, D. G., Larson, D. R., Liu, B. and Liu, R., Operator-valued measures, dilations, and the theory of frames, Mem. Amer. Math. Soc., 229(1075), 2014.\ncitation_journal_title=J. Funct. Anal.; citation_title=Dilations for systems of imprmimitivity acting on Banach spaces; citation_author=D G Han, D R Larson, B Liu, R Liu; citation_volume=266; citation_publication_date=2014; citation_pages=6914-6937; citation_doi=10.1016\u002Fj.jfa.2014.02.040; citation_id=CR9\ncitation_title=Dilations of Frames, Operator Valued Measures and Bounded Linear Maps; citation_inbook_title=Contemp. Math.; citation_publication_date=2014; citation_pages=33-53; citation_id=CR10; citation_author=D G Han; citation_author=D R Larson; citation_author=B Liu; citation_author=R Liu; citation_publisher=Amer. Math. Soc.\ncitation_journal_title=J. Funct. Anal.; citation_title=Dilations of operator-valued measures with bounded p-variations and framings on Banach spaces; citation_author=D G Han, D R Larson, R Liu; citation_volume=274; citation_publication_date=2018; citation_pages=1466-1490; citation_doi=10.1016\u002Fj.jfa.2018.01.006; citation_id=CR11\ncitation_journal_title=Amer. J. Math.; citation_title=On the orthogonalization of operator representations; citation_author=R Kadison; citation_volume=77; citation_publication_date=1955; citation_pages=600-622; citation_doi=10.2307\u002F2372645; citation_id=CR12\ncitation_journal_title=Izv. Akad. Nauk SSSR Ser. Mat.; citation_title=Spectral functions of a symmetric operator; citation_author=M A Naimark; citation_volume=4; citation_publication_date=1940; citation_pages=277-318; citation_id=CR13\ncitation_journal_title=Dokl. Acad. Sci. SSSR; citation_title=On a representation of additive operator set functions; citation_author=M A Naimark; citation_volume=41; citation_publication_date=1943; citation_pages=373-375; citation_id=CR14\ncitation_title=Completely Bounded Maps and Operator Algebras; citation_publication_date=2002; citation_id=CR15; citation_author=V Paulsen; citation_publisher=Cambridge University Press\ncitation_journal_title=Proc. Amer. Math. Soc.; citation_title=Positive functions on C*-algebras; citation_author=W F Stinespring; citation_volume=6; citation_publication_date=1955; citation_pages=211-216; citation_id=CR16",{"EN":704},"Inspired by some recent development on the theory about projection valued dilations for operator valued measures or more generally bounded homomorphism dilations for bounded linear maps on Banach algebras, the authors explore a pure algebraic version of the dilation theory for linear systems acting on unital algebras and vector spaces. By introducing two natural dilation structures, namely the canonical and the universal dilation systems, they prove that every linearly minimal dilation is equivalent to a reduced homomorphism dilation of the universal dilation, and all the linearly minimal homomorphism dilations can be classified by the associated reduced subspaces contained in the kernel of synthesis operator for the universal dilation.",{"EN":706},"Structural Properties of Homomorphism Dilation Systems",{"VOID":708},"10.1007\u002Fs11401-020-0219-4","https:\u002F\u002Flink.springer.com\u002Farticle\u002F10.1007\u002Fs11401-020-0219-4","https:\u002F\u002Flink.springer.com\u002Fcontent\u002Fpdf\u002F10.1007\u002Fs11401-020-0219-4.pdf",[712,732,747,759],{"id":713,"sortIndex":21,"researcher":20,"roles":714,"affiliations":715,"properties":729},"1d613642-fcc2-4286-99ba-22b1204aa939",[197],[716],{"id":717,"sortIndex":21,"affiliation":718,"properties":726},"503595ed-a83a-47b7-aec0-a9a404153f41",{"id":719,"createTime":720,"updateTime":720,"relativeEntities":721,"slug":722,"properties":723,"entityType":49,"verifyStatus":19,"verifyTime":20,"verifyNote":20,"syncStatus":19,"languages":20,"translateLanguages":20,"viewCount":21},"8501b6a4-d9fd-426f-81db-49f50324eab0","2024-04-14T19:10:53.999+00:00",[],"Department-of-Mathematics-University-of-Central-Florida-Orlando-U-S-A",{"title":724},{"EN":725},"Department of Mathematics, University of Central Florida, Orlando, U.S.A",{"title":727},{"VI":728},"Department of Mathematics, University of Central Florida, Orlando, USA",{"title":730},{"VI":731},"Han, Deguang",{"id":733,"sortIndex":121,"researcher":20,"roles":734,"affiliations":735,"properties":744},"ec03fbfd-0cb6-47c4-a2b8-259963725824",[197],[736],{"id":20,"sortIndex":21,"affiliation":737,"properties":20},{"id":738,"createTime":739,"updateTime":739,"relativeEntities":740,"slug":20,"properties":741,"entityType":49,"verifyStatus":19,"verifyTime":20,"verifyNote":20,"syncStatus":19,"languages":20,"translateLanguages":20,"viewCount":21},"83a83e04-19b1-487b-9e92-d534cf9fc789","2024-01-08T08:02:33.553+00:00",[],{"title":742},{"VI":743},"Department of Mathematics, Texas A&M University, College Station, USA",{"title":745},{"VI":746},"Larson, David R.",{"id":748,"sortIndex":62,"researcher":20,"roles":749,"affiliations":750,"properties":756},"9eb6003f-437d-412d-b7a9-562103b37305",[197],[751],{"id":20,"sortIndex":21,"affiliation":752,"properties":20},{"id":304,"createTime":305,"updateTime":305,"relativeEntities":753,"slug":20,"properties":754,"entityType":49,"verifyStatus":19,"verifyTime":20,"verifyNote":20,"syncStatus":19,"languages":20,"translateLanguages":20,"viewCount":21},[],{"title":755},{"VI":309},{"title":757},{"VI":758},"Liu, 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Bei",{"url":709,"publisher":775,"properties":803},{"id":6,"createTime":7,"updateTime":8,"relativeEntities":776,"slug":10,"properties":777,"entityType":18,"verifyStatus":19,"verifyTime":20,"verifyNote":20,"syncStatus":19,"languages":20,"translateLanguages":20,"viewCount":21,"subjectFields":781,"manageAffiliations":782,"indexDatabases":783,"url":104,"thumbnailPath":20,"statistic":798,"gsStatistic":20,"type":173,"analyzePriority":20},[],{"issn":778,"eissn":779,"title":780},{"VOID":13},{"VOID":15},{"EN":17},[],[],[784,791],{"id":86,"indexDatabase":785,"url":101,"indexYears":20,"academicFieldIds":790,"indexDatabaseRanking":20},{"id":88,"createTime":89,"updateTime":90,"relativeEntities":786,"label":787,"description":788,"key":97,"publicationTags":789,"standard":20},[],{"EN":93,"VI":93},{"VI":95,"EN":96},[99,100],[103],{"id":66,"indexDatabase":792,"url":79,"indexYears":80,"academicFieldIds":797,"indexDatabaseRanking":84},{"id":68,"createTime":69,"updateTime":70,"relativeEntities":793,"label":794,"description":795,"key":76,"publicationTags":796,"standard":20},[],{"EN":73,"VI":73},{"EN":73,"VI":75},[78],[82,83],{"impactFactor":21,"impactFactorByYear":799,"i10Index":118,"i10IndexLast5Year":21,"totalPublication":119,"totalPublicationByYear":800,"totalCitation":140,"totalCitationByYear":801,"totalCitationPerPublication":154,"totalCitationPerPublicationByYear":802,"hindexLast5Year":172,"hindex":172},{"2012":107,"2013":108,"2014":109,"2015":110,"2016":111,"2017":112,"2018":113,"2019":114,"2020":110,"2021":115,"2022":116,"2023":117},{"1999":121,"2000":122,"2006":123,"2007":124,"2008":125,"2009":126,"2010":127,"2011":128,"2012":129,"2013":130,"2014":131,"2015":132,"2016":133,"2017":132,"2018":134,"2019":135,"2020":136,"2021":130,"2022":137,"2023":138,"2024":139},{"1999":142,"2006":137,"2007":143,"2008":144,"2009":145,"2010":146,"2011":125,"2012":147,"2013":148,"2014":138,"2015":149,"2016":139,"2017":150,"2018":151,"2019":152,"2020":153,"2021":50,"2022":152,"2023":122},{"1999":142,"2006":156,"2007":157,"2008":158,"2009":159,"2010":160,"2011":161,"2012":162,"2013":163,"2014":164,"2015":165,"2016":166,"2017":167,"2018":168,"2019":169,"2020":170,"2021":171,"2022":113,"2023":116},{"volume":804,"pages":805,"issue":807},{"VOID":528},{"VOID":806},"585-600",{"VOID":808},"4","2020-07-01",{"id":811,"createTime":812,"updateTime":813,"relativeEntities":814,"slug":815,"properties":816,"entityType":191,"verifyStatus":294,"verifyTime":813,"verifyNote":295,"syncStatus":19,"languages":20,"translateLanguages":20,"viewCount":21,"primaryUrl":825,"fullTextUrl":20,"authors":826,"publicationType":241,"publisherRelationship":859,"citationCount":20,"citationInfo":20,"publishDate":893,"publishYear":894,"citationAnalyzeStatus":19,"lastCitationAnalyze":20,"indexDatabases":20,"openAccess":20,"references":20,"isForceReanalyzing":278},"465640cd-c6f9-45d3-8d0f-11c06cf64981","2023-12-08T18:53:23.811+00:00","2024-12-21T23:45:57.446+00:00",[],"Symmetries-and-their-lie-algebra-of-a-variable-coefficient-Korteweg-de-Vries-hierarchy",{"references":817,"abstract":819,"title":821,"doi":823},{"VOID":818},"Grimshaw, R., Slowly varying solitary waves, I. Korteweg-de Vries equation, Proc. Royal Soc. Lon. A-Math. Phys. Engin. Sci., 368, 1979, 359–375.\nJoshi, N., Painlevé property of general variable-coefficient versions of the Korteweg-de Vries and nonlinear Schrödinger equations, Phys. Lett. A, 125, 1987, 456–460.\nZhang, Y. C., Yao, Z. Z., Zhu, H. W., et al., Exact analytic N-soliton-like solution in Wronskian form for a generalized variable-coefficient Korteweg-de Vries model from plasmas and fluid dynamics, Chin. Phys. Lett., 24, 2007, 1173–1176.\nZhang, Y. C., Li, J., Meng, X. H., et al., Existence of formal conservation laws of a variable-coefficient Korteweg-de Vries equation from fluid dynamics and plasma physics via symbolic computation, Chin. Phys. Lett., 25, 2008, 878–880.\nZhang, D. J., Conservation laws and Lax pair of the variable coefficient KdV equation, Chin. Phys. Lett., 24, 2007, 3021–3023.\nHong, W. and Jung, Y. D., Auto-Bäcklund transformation and analytic solutions for general variablecoefficient KdV equation, Phys. Lett. A, 257, 1999, 149–152.\nFan, E. G., Auto-Bäcklund transformation and similarity reductions for general variable coefficient KdV equations, Phys. Lett. A, 294, 2002, 26–30.\nFuchssteiner, B. and Fokas, A., Symplectic structures, their Bäcklund transformations and hereditary symmetries, Physica D, 4, 1981, 47–66.\nFuchssteiner, B., Application of hereditary symmetries to nonlinear evolution equations, Nonlinear Analysis, TMA, 3, 1979, 849–862.\nMa, W. X., K-symmetries and t-symmetries of evolution equations and their Lie algebras, J. Phys. A: Math. Gen., 23, 1990, 2707–2716.\nMa, W. X., The algebraic structures of isospectral Lax operators and applications to integrable equations, J. Phys. A: Math. Gen., 25, 1992, 5329–5343.\nMa, W. X., Lax representations and Lax operator algebras of isospectral and nonisospectral hierarchies of evolution equations, J. Math. Phys., 33, 1992, 2464–2476.\nMa, W. X. and Fuchssteiner, B., Algebraic structure of discrete zero curvature equations and master symmetries of discrete evolution equations, J. Math. Phys., 40, 1999, 2400–2418.\nTamizhmani, K. and Ma, W. X., Master symmetries from Lax operators for certain lattice soliton hierarchies, J. Phys. Soc. Jpn., 69, 2000, 351–361.\nChen, D. Y. and Zhang, H. W., Lie algebraic structure for the AKNS system, J. Phys. A: Gen. Math. Phys., 24, 1991, 377–383.\nChen, D. Y. and Zhang, D. J., Lie algebraic structures of (1+1)-dimensional Lax integrable systems, J. Math. Phys., 37, 1996, 5524–5538.\nTian, C., Symmetries, in Soliton Theory and Its Applications, Gu C. H. ed., Springer-Verlag, Berlin, 1996.\nFuchssteiner, B., Master symmetries, higher order time-dependent symmetries and conserved densities of nonlinear evolution equations, Prog. Theo. Phys., 70, 1983, 1508–1522.",{"EN":820},"Isospectral and non-isospectral hierarchies related to a variable coefficient Painlevé integrable Korteweg-de Vries (KdV for short) equation are derived. The hierarchies share a formal recursion operator which is not a rigorous recursion operator and contains t explicitly. By the hereditary strong symmetry property of the formal recursion operator, the authors construct two sets of symmetries and their Lie algebra for the isospectral variable coefficient Korteweg-de Vries (vcKdV for short) hierarchy.",{"EN":822},"Symmetries and their lie algebra of a variable coefficient Korteweg-de Vries hierarchy",{"VOID":824},"10.1007\u002Fs11401-016-1020-2","http:\u002F\u002Flink.springer.com\u002F10.1007\u002Fs11401-016-1020-2",[827,842],{"id":828,"sortIndex":21,"researcher":20,"roles":829,"affiliations":830,"properties":839},"1ebd2558-6e7e-4e0b-8d41-99801e86b43a",[197],[831],{"id":20,"sortIndex":21,"affiliation":832,"properties":20},{"id":833,"createTime":834,"updateTime":834,"relativeEntities":835,"slug":20,"properties":836,"entityType":49,"verifyStatus":19,"verifyTime":20,"verifyNote":20,"syncStatus":19,"languages":20,"translateLanguages":20,"viewCount":21},"651471ac-57b4-47e6-8034-a170317b9910","2023-12-08T18:53:23.823+00:00",[],{"title":837},{"VI":838},"College of Sciences, Shandongjianzhu University, Jinan, China",{"title":840},{"VI":841},"Xiaoying Zhu",{"id":843,"sortIndex":121,"researcher":20,"roles":844,"affiliations":845,"properties":856},"65ef20df-5fde-48d4-b948-d526ed7ba1ac",[197],[846],{"id":20,"sortIndex":21,"affiliation":847,"properties":20},{"id":848,"createTime":849,"updateTime":850,"relativeEntities":851,"slug":852,"properties":853,"entityType":49,"verifyStatus":19,"verifyTime":20,"verifyNote":20,"syncStatus":19,"languages":20,"translateLanguages":20,"viewCount":21},"b1542030-2821-49ea-88d0-f40add65aaa9","2024-02-17T00:11:25.799+00:00","2024-10-14T06:02:22.981+00:00",[],"Department-of-Mathematics-Shanghai-University-Shanghai-China",{"title":854},{"VI":855},"Department of Mathematics, Shanghai University, Shanghai, China",{"title":857},{"VI":858},"Dajun Zhang",{"url":825,"publisher":860,"properties":888},{"id":6,"createTime":7,"updateTime":8,"relativeEntities":861,"slug":10,"properties":862,"entityType":18,"verifyStatus":19,"verifyTime":20,"verifyNote":20,"syncStatus":19,"languages":20,"translateLanguages":20,"viewCount":21,"subjectFields":866,"manageAffiliations":867,"indexDatabases":868,"url":104,"thumbnailPath":20,"statistic":883,"gsStatistic":20,"type":173,"analyzePriority":20},[],{"issn":863,"eissn":864,"title":865},{"VOID":13},{"VOID":15},{"EN":17},[],[],[869,876],{"id":86,"indexDatabase":870,"url":101,"indexYears":20,"academicFieldIds":875,"indexDatabaseRanking":20},{"id":88,"createTime":89,"updateTime":90,"relativeEntities":871,"label":872,"description":873,"key":97,"publicationTags":874,"standard":20},[],{"EN":93,"VI":93},{"VI":95,"EN":96},[99,100],[103],{"id":66,"indexDatabase":877,"url":79,"indexYears":80,"academicFieldIds":882,"indexDatabaseRanking":84},{"id":68,"createTime":69,"updateTime":70,"relativeEntities":878,"label":879,"description":880,"key":76,"publicationTags":881,"standard":20},[],{"EN":73,"VI":73},{"EN":73,"VI":75},[78],[82,83],{"impactFactor":21,"impactFactorByYear":884,"i10Index":118,"i10IndexLast5Year":21,"totalPublication":119,"totalPublicationByYear":885,"totalCitation":140,"totalCitationByYear":886,"totalCitationPerPublication":154,"totalCitationPerPublicationByYear":887,"hindexLast5Year":172,"hindex":172},{"2012":107,"2013":108,"2014":109,"2015":110,"2016":111,"2017":112,"2018":113,"2019":114,"2020":110,"2021":115,"2022":116,"2023":117},{"1999":121,"2000":122,"2006":123,"2007":124,"2008":125,"2009":126,"2010":127,"2011":128,"2012":129,"2013":130,"2014":131,"2015":132,"2016":133,"2017":132,"2018":134,"2019":135,"2020":136,"2021":130,"2022":137,"2023":138,"2024":139},{"1999":142,"2006":137,"2007":143,"2008":144,"2009":145,"2010":146,"2011":125,"2012":147,"2013":148,"2014":138,"2015":149,"2016":139,"2017":150,"2018":151,"2019":152,"2020":153,"2021":50,"2022":152,"2023":122},{"1999":142,"2006":156,"2007":157,"2008":158,"2009":159,"2010":160,"2011":161,"2012":162,"2013":163,"2014":164,"2015":165,"2016":166,"2017":167,"2018":168,"2019":169,"2020":170,"2021":171,"2022":113,"2023":116},{"volume":889,"pages":891},{"VOID":890},"37",{"VOID":892},"543-552","2016-06-29",2016,{"id":896,"createTime":897,"updateTime":898,"relativeEntities":899,"slug":900,"properties":901,"entityType":191,"verifyStatus":294,"verifyTime":910,"verifyNote":295,"syncStatus":19,"languages":20,"translateLanguages":20,"viewCount":21,"primaryUrl":911,"fullTextUrl":20,"authors":912,"publicationType":241,"publisherRelationship":930,"citationCount":20,"citationInfo":20,"publishDate":964,"publishYear":965,"citationAnalyzeStatus":19,"lastCitationAnalyze":20,"indexDatabases":20,"openAccess":20,"references":20,"isForceReanalyzing":278},"43bb45c5-c0fa-499a-9e85-004ea1c9e721","2023-12-27T13:54:52.832+00:00","2025-01-19T23:43:22.607+00:00",[],"On-a-Lotka-Volterra-Competition-Diffusion-Model-with-Advection",{"references":902,"abstract":904,"title":906,"doi":908},{"VOID":903},"Averill, I., Lam, K.-Y. and Lou, Y., The role of advection in a two-species competition model: A bifurcation approach, Mem. Amer. Math. Soc., 245(1161), 2017, v+ 117 pp.\nCantrell, R. S. and Cosner, C., Spatial Ecology Via Reaction-Diffusion Equations, Series in Mathematical and Computational Biology, Wiley, Chichester, UK, 2003.\nCantrell, R. S., Cosner, C. and Lou, Y., Multiple reversals of competitive dominance in ecological reserves via external habitat degradation, J. Dynam. Differential Equations, 16, 2004, 973–1010.\nCantrell, R. S., Cosner, C. and Lou, Y., Movement toward better environments and the evolution of rapid diffusion, Math. Biosci., 204, 2006, 199–214.\nCantrell, R. S., Cosner, C. and Lou, Y., Advection-mediated coexistence of competing species, Proc. Roy. Soc. Edinburgh Sect. A, 137, 2007, 497–518.\nChen, X. F., Hambrock, R. and Lou, Y., Evolution of conditional dispersal: A reaction-diffusion-advection model, J. Math. Biol., 57, 2008, 361–386.\nCosner, C. and Lou, Y., When does movement toward better environment benefit a population? J. Math. Anal. Appl., 277, 2003, 489–503.\nDu, Y., Effects of a degeneracy in the competition model, Part I, Classical and generalized steady-state solutions, J. Differential Equations, 181, 2002, 92–132.\nDu, Y., Effects of a degeneracy in the competition model, Part II, Perturbation and dynamical behavior, J. Differential Equations, 181, 2002, 133–164.\nDu, Y., Realization of prescribed patterns in the competition model, J. Differential Equations, 193, 2003, 147–179.\nEvans, L. C., Partial Differential Equations, Graduate Studies in Mathematics, 19, American Mathematical Society, USA, 1999.\nLópez-Gómez, J., Coexistence and meta-coexistence for competing species, Houston J. Math., 29(2), 2003, 483–536.\nHambrock, R. and Lou, Y., The evolution of conditional dispersal strategies in spatially heterogeneous habitats, Bull. Math. Biol., 71, 2009, 1793–1817.\nHe, X. and Ni, W.-M., Global dynamics of the Lotka-Volterra competition-diffusion system: Diffusion and spatial heterogeneity I, Comm. Pure Appl. Math., 69, 2016, 981–1014.\nHe, X. and Ni, W.-M., Global dynamics of the Lotka-Volterra competition-diffusion system with equal amount of total resources, II, Calc. Var. Partial Differential Equations, 55, 2016, 25, 20 pp.\nHe, X., and Ni W.-M., Global dynamics of the Lotka-Volterra competition-diffusion system with equal amount of total resources, III, Calc. Var. Partial Differential Equations, 56, 2017, 132, 26 pp.\nHess, P., Periodic-parabolic Boundary Value Problems and Positivity, Pitman Research Notes in Mathematics, 247. Longman Sci. Tech., Harlow, 1991.\nHutson, V., Lou, Y. and Mischaikow, K., Spatial heterogeneity of resources versus Lotka-Volterra dynamics, J. Differential Equations, 185, 2002, 97–136.\nHutson, V., Lou, Y. and Mischaikow, K., Convergence in competition models with small diffusion coeffcients, J. Differential Equations, 211, 2005, 135–161.\nHutson, V., Lou, Y. and Mischaikow, K., Poláčik, P., Competing species near the degenerate limit, SIAM J. Math. Anal., 35, 2003, 453–491.\nHutson, V., Martinez, S., Mischaikow, K. and Vicker, G. T., The evolution of dispersal, J. Math. Biol., 47, 2003, 483–517.\nHutson, V., Mischaikow, K. and Poláčik, P., The evolution of dispersal rates in a heterogeneous time-periodic environment, J. Math. Biol., 43, 2001, 501–533.\nLam, K.-Y., Concentration phenomena of a semilinear elliptic equation with large advection in an ecological model, J. Differential Equations, 250, 2011, 161–181.\nLam, K.-Y., Limiting profiles of semilinear elliptic equations with large advection in population dynamics II, SIAM J. Math. Anal., 44, 2012, 1808–1830.\nLou, Y., On the effects of migration and spatial heterogeneity on single and multiple species, J. Differential Equations, 223, 2006, 400–426.\nLou, Y., Martinez, S. and Poláčik, P., Loops and branches of coexistence states in a Lotka-Volterra competition model, J. Differential Equations, 230, 2006, 720–742.\nProtter, M. H. and Weinberger, H. F., Maximum Principles in Differential Equations, 2nd ed., Springer-Verlag, New York, 1984.\nSaut, J. C. and Scheurer, B., Remarks on a nonlinear equation arising in population genetics, Commun. Part. Differ. Eq., 23, 1978, 907–931.\nSattinger, D. H., Monotone methods in nonlinear elliptic and parabolic boundary value problems, Indiana Univ. Math. J., 21, 1972, 979–1000.\nWang, Q., On steady state of some Lotka-Volterra competition-diffusion-advection model, Discrete Contin. Dyn. Syst. Ser. B, 25, 2020, 859–875.\nZhou, P. and Xiao, D., Global dynamics of a classical Lotka-Volterra competition-diffusion-advection system, J. Funct. Anal., 275, 2018, 356–380.",{"EN":905},"In this paper, the author focuses on the joint effects of diffusion and advection on the dynamics of a classical two species Lotka-Volterra competition-diffusion-advection system, where the ratio of diffusion and advection rates are supposed to be a positive constant. For comparison purposes, the two species are assumed to have identical competition abilities throughout this paper. The results explore the condition on the diffusion and advection rates for the stability of former species. Meanwhile, an asymptotic behavior of the stable coexistence steady states is obtained.",{"EN":907},"On a Lotka-Volterra Competition Diffusion Model with Advection",{"VOID":909},"10.1007\u002Fs11401-021-0296-z","2025-01-19T23:43:22.606+00:00","https:\u002F\u002Flink.springer.com\u002Farticle\u002F10.1007\u002Fs11401-021-0296-z",[913],{"id":914,"sortIndex":21,"researcher":20,"roles":915,"affiliations":916,"properties":927},"441765ab-3596-46f7-bfaa-7036d42dbbf1",[197],[917],{"id":20,"sortIndex":21,"affiliation":918,"properties":20},{"id":919,"createTime":920,"updateTime":921,"relativeEntities":922,"slug":923,"properties":924,"entityType":49,"verifyStatus":19,"verifyTime":20,"verifyNote":20,"syncStatus":19,"languages":20,"translateLanguages":20,"viewCount":21},"3adf4669-1103-477e-95fc-8198c18918fc","2023-12-26T02:02:44.509+00:00","2024-10-14T12:07:39.316+00:00",[],"College-of-Science-University-of-Shanghai-for-Science-and-Technology-Shanghai-China",{"title":925},{"VI":926},"College of Science, University of Shanghai for Science and Technology, Shanghai, China",{"title":928},{"VI":929},"Qi Wang",{"url":911,"publisher":931,"properties":959},{"id":6,"createTime":7,"updateTime":8,"relativeEntities":932,"slug":10,"properties":933,"entityType":18,"verifyStatus":19,"verifyTime":20,"verifyNote":20,"syncStatus":19,"languages":20,"translateLanguages":20,"viewCount":21,"subjectFields":937,"manageAffiliations":938,"indexDatabases":939,"url":104,"thumbnailPath":20,"statistic":954,"gsStatistic":20,"type":173,"analyzePriority":20},[],{"issn":934,"eissn":935,"title":936},{"VOID":13},{"VOID":15},{"EN":17},[],[],[940,947],{"id":86,"indexDatabase":941,"url":101,"indexYears":20,"academicFieldIds":946,"indexDatabaseRanking":20},{"id":88,"createTime":89,"updateTime":90,"relativeEntities":942,"label":943,"description":944,"key":97,"publicationTags":945,"standard":20},[],{"EN":93,"VI":93},{"VI":95,"EN":96},[99,100],[103],{"id":66,"indexDatabase":948,"url":79,"indexYears":80,"academicFieldIds":953,"indexDatabaseRanking":84},{"id":68,"createTime":69,"updateTime":70,"relativeEntities":949,"label":950,"description":951,"key":76,"publicationTags":952,"standard":20},[],{"EN":73,"VI":73},{"EN":73,"VI":75},[78],[82,83],{"impactFactor":21,"impactFactorByYear":955,"i10Index":118,"i10IndexLast5Year":21,"totalPublication":119,"totalPublicationByYear":956,"totalCitation":140,"totalCitationByYear":957,"totalCitationPerPublication":154,"totalCitationPerPublicationByYear":958,"hindexLast5Year":172,"hindex":172},{"2012":107,"2013":108,"2014":109,"2015":110,"2016":111,"2017":112,"2018":113,"2019":114,"2020":110,"2021":115,"2022":116,"2023":117},{"1999":121,"2000":122,"2006":123,"2007":124,"2008":125,"2009":126,"2010":127,"2011":128,"2012":129,"2013":130,"2014":131,"2015":132,"2016":133,"2017":132,"2018":134,"2019":135,"2020":136,"2021":130,"2022":137,"2023":138,"2024":139},{"1999":142,"2006":137,"2007":143,"2008":144,"2009":145,"2010":146,"2011":125,"2012":147,"2013":148,"2014":138,"2015":149,"2016":139,"2017":150,"2018":151,"2019":152,"2020":153,"2021":50,"2022":152,"2023":122},{"1999":142,"2006":156,"2007":157,"2008":158,"2009":159,"2010":160,"2011":161,"2012":162,"2013":163,"2014":164,"2015":165,"2016":166,"2017":167,"2018":168,"2019":169,"2020":170,"2021":171,"2022":113,"2023":116},{"volume":960,"pages":962},{"VOID":961},"42",{"VOID":963},"891-908","2021-11-12",2021,{"id":967,"createTime":968,"updateTime":969,"relativeEntities":970,"slug":971,"properties":972,"entityType":191,"verifyStatus":294,"verifyTime":969,"verifyNote":295,"syncStatus":19,"languages":20,"translateLanguages":20,"viewCount":21,"primaryUrl":981,"fullTextUrl":20,"authors":982,"publicationType":241,"publisherRelationship":1013,"citationCount":20,"citationInfo":20,"publishDate":1046,"publishYear":693,"citationAnalyzeStatus":19,"lastCitationAnalyze":20,"indexDatabases":20,"openAccess":20,"references":20,"isForceReanalyzing":278},"9e659a1f-e4bf-4a3b-8358-18b189984d35","2024-02-22T03:14:58.262+00:00","2024-12-05T23:42:59.378+00:00",[],"Quasi-sure-flows-associated-with-vector-fields-of-low-regularity",{"references":973,"abstract":975,"title":977,"doi":979},{"VOID":974},"Ambrosio, L. and Figalli, A., On flows associated to Sobolev vector fields in Wiener space: an approach à la Di Perna-Lions, J. Funct. Anal., 256(1), 2009, 179–214.\nBogachev, V. I., Gaussian Measures, Mathematical Suverys and Monographs, 62, American Mathematical Society, Providence, RI, 1998.\nCruzeiro, A. B., Équations différentielles sur l’espace de Wiener et formules de Cameron-Martin nonlin éaires, J. Funct. Anal., 54, 1983, 206–227.\nCruzeiro, A. B., Unicité de solutions d’équations différentielles sur l’espace de Wiener, J. Funct. Anal., 58, 1984, 335–347.\nDenis, L., Quasi-sure analysis related to sub-Markovian semi-group, Potential Anal., 6, 1997, 289–311.\nGross, L., Abstract Wiener spaces, in“Proc. Fifth Berkeley Sympos. Math. Statist. and Prob.”, University of California Press, Berkeley, CA, 1 (1), 1965, 31–42.\nHuang, Z. Y. and Yan, J. A., Introduction to Infinite Dimensional Stochastic Analysis, Monographs in Pure and Appl. Mathematics, Chinese Academic Press, Beijing, 37, 1997 (in Chinese).\nKusuoka, S., Analysis on Wiener space. I. Nonlinear maps, J. Funct. Anal., 98, 1998, 122–168.\nMalliavin, P. and Nualart, D., Quasi-sure analysis and Stratonovich anticipative stochastic differential equations, Probab. Theory Relat. Fields, 78, 1993, 45–55.\nMalliavin, P., Stochastic Analysis, Grund. Math. Wissen., 313, Springer-Verlag, Berlin, 1997.\nPeters, G., Anticipating flows on the Wiener space generated by vector fields of low regularity, J. Funct. Anal., 142, 1996, 129–192.\nRen, J. G., Analyse quasi-sûre des équations différentielles stochastiques, Bull. Sci. Math. II. Sér., 114, 1990, 187–213.\nShigekawa, I., Sobolev spaces of Banach valued functions associated with a Markov processes, Probab. Theory Relat. Fields, 99, 1994, 425–441.\nYun, Y. S., The quasi-sure existence of solutions for differential equations on Wiener space, J. Kyoto. Univ., 34(4), 1994, 767–796.\nYun, Y. S., A quasi-sure flow property and the equivalence of capacities for differential equations on the Wiener space, J. Funct. Anal., 137, 1996, 381–393.",{"EN":976},"The authors construct a solution U\n                \n                  t\n                (x) associated with a vector field on the Wiener space for all initial values except in a 1-slim set and obtain the 1-quasi-sure flow property where the vector field is a sum of a skew-adjoint operator not necessarily bounded and a nonlinear part with low regularity, namely one-fold differentiability. Besides, the equivalence of capacities under the transformations of the Wiener space induced by the solutions is obtained.",{"EN":978},"Quasi-sure flows associated with vector fields of low regularity",{"VOID":980},"10.1007\u002Fs11401-013-0816-6","https:\u002F\u002Flink.springer.com\u002Farticle\u002F10.1007\u002Fs11401-013-0816-6",[983,998],{"id":984,"sortIndex":121,"researcher":20,"roles":985,"affiliations":986,"properties":995},"48d2694d-e50b-4dfb-90a4-13fd47cf6d58",[197],[987],{"id":20,"sortIndex":21,"affiliation":988,"properties":20},{"id":989,"createTime":990,"updateTime":990,"relativeEntities":991,"slug":20,"properties":992,"entityType":49,"verifyStatus":19,"verifyTime":20,"verifyNote":20,"syncStatus":19,"languages":20,"translateLanguages":20,"viewCount":21},"8df5bd36-863c-4234-8783-fc39ac106452","2024-01-11T03:59:06.739+00:00",[],{"title":993},{"VI":994},"School of Statistics, Jiangxi University of Finance and Economics, Nanchang, China",{"title":996},{"VI":997},"Hua Zhang",{"id":999,"sortIndex":21,"researcher":20,"roles":1000,"affiliations":1001,"properties":1010},"3be97628-96ed-44f0-88c8-8447d759e7ae",[197],[1002],{"id":20,"sortIndex":21,"affiliation":1003,"properties":20},{"id":1004,"createTime":1005,"updateTime":1005,"relativeEntities":1006,"slug":20,"properties":1007,"entityType":49,"verifyStatus":19,"verifyTime":20,"verifyNote":20,"syncStatus":19,"languages":20,"translateLanguages":20,"viewCount":21},"cce96c4b-7d2d-46ca-ac56-de9a89636f4a","2024-02-22T03:14:58.281+00:00",[],{"title":1008},{"VI":1009},"Faculty of Sciences, Ningbo University, Ningbo, Zhejiang, China",{"title":1011},{"VI":1012},"Siyan Xu",{"url":981,"publisher":1014,"properties":1042},{"id":6,"createTime":7,"updateTime":8,"relativeEntities":1015,"slug":10,"properties":1016,"entityType":18,"verifyStatus":19,"verifyTime":20,"verifyNote":20,"syncStatus":19,"languages":20,"translateLanguages":20,"viewCount":21,"subjectFields":1020,"manageAffiliations":1021,"indexDatabases":1022,"url":104,"thumbnailPath":20,"statistic":1037,"gsStatistic":20,"type":173,"analyzePriority":20},[],{"issn":1017,"eissn":1018,"title":1019},{"VOID":13},{"VOID":15},{"EN":17},[],[],[1023,1030],{"id":86,"indexDatabase":1024,"url":101,"indexYears":20,"academicFieldIds":1029,"indexDatabaseRanking":20},{"id":88,"createTime":89,"updateTime":90,"relativeEntities":1025,"label":1026,"description":1027,"key":97,"publicationTags":1028,"standard":20},[],{"EN":93,"VI":93},{"VI":95,"EN":96},[99,100],[103],{"id":66,"indexDatabase":1031,"url":79,"indexYears":80,"academicFieldIds":1036,"indexDatabaseRanking":84},{"id":68,"createTime":69,"updateTime":70,"relativeEntities":1032,"label":1033,"description":1034,"key":76,"publicationTags":1035,"standard":20},[],{"EN":73,"VI":73},{"EN":73,"VI":75},[78],[82,83],{"impactFactor":21,"impactFactorByYear":1038,"i10Index":118,"i10IndexLast5Year":21,"totalPublication":119,"totalPublicationByYear":1039,"totalCitation":140,"totalCitationByYear":1040,"totalCitationPerPublication":154,"totalCitationPerPublicationByYear":1041,"hindexLast5Year":172,"hindex":172},{"2012":107,"2013":108,"2014":109,"2015":110,"2016":111,"2017":112,"2018":113,"2019":114,"2020":110,"2021":115,"2022":116,"2023":117},{"1999":121,"2000":122,"2006":123,"2007":124,"2008":125,"2009":126,"2010":127,"2011":128,"2012":129,"2013":130,"2014":131,"2015":132,"2016":133,"2017":132,"2018":134,"2019":135,"2020":136,"2021":130,"2022":137,"2023":138,"2024":139},{"1999":142,"2006":137,"2007":143,"2008":144,"2009":145,"2010":146,"2011":125,"2012":147,"2013":148,"2014":138,"2015":149,"2016":139,"2017":150,"2018":151,"2019":152,"2020":153,"2021":50,"2022":152,"2023":122},{"1999":142,"2006":156,"2007":157,"2008":158,"2009":159,"2010":160,"2011":161,"2012":162,"2013":163,"2014":164,"2015":165,"2016":166,"2017":167,"2018":168,"2019":169,"2020":170,"2021":171,"2022":113,"2023":116},{"volume":1043,"pages":1044},{"VOID":689},{"VOID":1045},"51-68","2014-02-01"]