Entire solutions in the Fisher-KPP equation with nonlocal dispersal

Nonlinear Analysis: Real World Applications - Tập 11 Số 4 - Trang 2302-2313 - 2010
Wan‐Tong Li1, Yujuan Sun1, Zhi-Cheng Wang1
1School of Mathematics and Statistics, Lanzhou University, Lanzhou, Gansu 730000, People's Republic of China

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Tài liệu tham khảo

Schumacher, 1980, Travelling-front solutions for integro-differential equations, I, J. Reine Angew. Math, 316, 54, 10.1515/crll.1980.316.54

Carr, 2004, Uniqueness of travelling waves for nonlocal monostable equations, Proc. Amer. Math. Soc., 132, 2433, 10.1090/S0002-9939-04-07432-5

Coville, 2007, On a nonlocal reaction diffusion equation arising in population dynamics, Proc. Roy. Soc. Edinburgh Sect., 137A, 1

Atkinson, 1976, Deterministic epidemic waves, Math. Proc. Cambridge Philos. Soc., 80, 315, 10.1017/S0305004100052944

Bates, 1997, Traveling waves in a convolution model for phase transition, Arch. Ration. Mech. Anal., 138, 105, 10.1007/s002050050037

Berestycki, 1991, On the method of moving planes and the sliding method, Bol. da Soc. Brasileira de Math, 22, 1, 10.1007/BF01244896

Berestycki, 1992, Travelling fronts in cylinder, Ann. Inst. Henri Poincaré, 9, 497, 10.1016/S0294-1449(16)30229-3

Berestycki, 1985, Travelling wave solutions to combustion models and their singular limits, SIAM J. Math. Anal, 16, 1207, 10.1137/0516088

Brown, 1977, Deterministic epidemic waves of critical velocity, Math. Proc. Cambridge Philos. Soc., 81, 431, 10.1017/S0305004100053494

Chen, 1997, Existence, uniqueness and asymptotical stability of travelling fronts in non-local evolution equations, Adv. Differential Equations, 2, 125, 10.57262/ade/1366809230

J. Coville, Travelling fronts in asymmetric nonlocal reaction diffusion equation: The bistable and ignition case, (Preprint)

Fife, 1977, The approach of solutions of nonlinear diffusion equation to travelling front solutions, Arch. Ration. Mech. Anal., 65, 335, 10.1007/BF00250432

Pan, 2008, Traveling wave fronts of delayed non-local diffusion systems without quasimonotonicity, J. Math. Anal. Appl., 346, 415, 10.1016/j.jmaa.2008.05.057

Pan, 2009, Travelling wave fronts in nonlocal reaction-diffusion systems and applications, Z. Angew. Math. Phys., 60, 377, 10.1007/s00033-007-7005-y

Wang, 2006, Travelling wave fronts of reaction-diffusion systems with spatio-temporal delays, J. Differential Equations, 222, 185, 10.1016/j.jde.2005.08.010

Wang, 2007, Existence and stability of traveling wave fronts in reaction advection diffusion equations, J. Differential Equations, 238, 153, 10.1016/j.jde.2007.03.025

Wang, 2008, Traveling fronts in monostable equations with nonlocal delayed effects, J. Dynam. Differential Equations, 20, 563, 10.1007/s10884-008-9103-8

Morita, 2006, Entire solutions with merging fronts to reaction-diffusion equations, J. Dynam. Differential Equations, 18, 841, 10.1007/s10884-006-9046-x

Chen, 2005, Existence and uniqueness of entire solutions for a reaction-diffusion equation, J. Differential Equations, 212, 62, 10.1016/j.jde.2004.10.028

Chen, 2006, Entire solutions of reaction-diffusion equations with balanced bistable nonlinearities, Proc. Roy. Soc. Edinburgh, 136A, 1207, 10.1017/S0308210500004959

Fukao, 2004, Some entire solutions of the Allen–Cahn equation, Taiwanese J. Math., 8, 15, 10.11650/twjm/1500558454

Guo, 2005, Entire solutions of reaction-diffusion equations and an application to discrete diffusive equations, Discrete Contin. Dyn. Syst., 12, 193, 10.3934/dcds.2005.12.193

Hamel, 1999, Entire solution of the KPP equation, Comm. Pure Appl. Math., 52, 1255, 10.1002/(SICI)1097-0312(199910)52:10<1255::AID-CPA4>3.0.CO;2-W

Hamel, 2001, Travelling fronts and entire solutions of the Fisher-KPP equation in RN, Arch. Ration. Mech. Anal., 157, 91, 10.1007/PL00004238

Li, 2008, Entire solutions in reaction-advection-diffusion equations in cylinders, J. Math. Pures Appl., 90, 492, 10.1016/j.matpur.2008.07.002

Li, 2008, Entire solutions in monostable reaction-diffusion equations with delayed nonlinearity, J. Differential Equations, 245, 102, 10.1016/j.jde.2008.03.023

Liu, 2009, Entire solutions of reaction-advection-diffusion equations with bistable nonlinearity in cylinders, J. Differential Equations, 246, 4249, 10.1016/j.jde.2008.12.005

Wang, 2009, Entire solutions in bistable reaction-diffusion equations with nonlocal delayed nonlinerity, Trans. Amer. Math. Soc., 361, 2047, 10.1090/S0002-9947-08-04694-1

Z.C. Wang, W.T. Li, S. Ruan, Entire solutions in lattice delayed differential equations with global interaction: Bistable case, Ann. Mat. Pur. Appl. (in press)

Wang, 2009, Entire solutions in delayed lattice differential equations with monostable nonlinearity, SIAM J. Math. Anal., 40, 2392, 10.1137/080727312

Yagisita, 2003, Backward global solutions characterizing annihilation dynamics of travelling fronts, Publ. Res. Inst. Math. Sci., 39, 117, 10.2977/prims/1145476150

Andreu, 2008, The Neumann problem for nonlocal nonlinear diffusion equations, J. Evol. Equ., 8, 189, 10.1007/s00028-007-0377-9

Cortazar, 2007, Boundary fluxes for non-local diffusion, J. Differential Equations, 234, 360, 10.1016/j.jde.2006.12.002

Gourley, 2006, Delayed nonlocal diffusive systems in biological invasion and disease spread, vol. 48, 137

Fife, 2003, Some nonclassical trends in parabolic and parabolic-like evolutions

Guo, 2008, Entire solutions for a discrete diffusive equation, J. Math. Anal. Appl., 347, 450, 10.1016/j.jmaa.2008.03.076

Chen, 2002, Almost periodic traveling waves of nonlocal evolution equations, Nonlinear Anal. TMA, 50, 807, 10.1016/S0362-546X(01)00787-8

Chen, 2002, Existence and asymptotic stability of travelling waves of discrete quasilinear monostable equations, J. Differential Equations, 184, 549, 10.1006/jdeq.2001.4153

Ma, 2005, Propagation and its failure in a lattice delayed differential equation with global interaction, J. Differential Equations, 212, 129, 10.1016/j.jde.2004.07.014

Weng, 2003, Asymptotic speed of propagation of wave fronts in a lattice delay differential equation with global interaction, IMA J. Appl. Math., 68, 409, 10.1093/imamat/68.4.409