Spreading speeds and traveling waves for abstract monostable evolution systems

Journal of Functional Analysis - Tập 259 - Trang 857-903 - 2010
Xing Liang1, Xiao-Qiang Zhao2
1Department of Mathematics, University of Science and Technology of China, Hefei, Anhui 230026, China
2Department of Mathematics and Statistics, Memorial University of Newfoundland, St. John's, NL, A1C 5S7, Canada

Tài liệu tham khảo

Aronson, 1975, Nonlinear diffusion in population genetics, combustion, and nerve pulse propagation, vol. 446, 5 Aronson, 1978, Multidimensional nonlinear diffusion arising in population dynamics, Adv. Math., 30, 33, 10.1016/0001-8708(78)90130-5 Berestycki, 2002, Front propagation in periodic excitable media, Comm. Pure Appl. Math., 55, 0949, 10.1002/cpa.3022 Berestycki, 2005, The speed of propagation for KPP type problems, I. Periodic framework, J. Eur. Math. Soc., 7, 173, 10.4171/JEMS/26 Berestycki, 2005, Analysis of the periodically fragmented environment model: II – biological invasions and pulsating traveling fronts, J. Math. Pures Appl., 84, 1101, 10.1016/j.matpur.2004.10.006 Fisher, 1937, The wave of advance of advantageous genes, Ann. Eugenics, 7, 335, 10.1111/j.1469-1809.1937.tb02153.x Freidlin, 1984, On wavefront propagation in periodic media, vol. 7 Garroni, 1992 Gärtner, 1979, On the propagation of concentration waves in periodic and random media, Sov. Math. Dokl., 20, 1282 Guo, 2006, Front propagation for discrete periodic monostable equations, Math. Ann., 335, 489, 10.1007/s00208-005-0729-0 Hadeler, 2002, Spatial dynamics of the diffusive logistic equation with a sedentary compartment, Can. Appl. Math. Q., 10, 473 Hale, 1988, Asymptotic Behavior of Dissipative Systems, vol. 25 Hudson, 1995, Existence of traveling waves for reaction–diffusion equations of Fisher type in periodic media, 187 Jin, 2009, Spacial dynamics of a discrete-time population model in a periodic lattics habitat, J. Dynam. Differential Equations, 21, 501, 10.1007/s10884-009-9138-5 Kolmogorov, 1937, Etude de lequation de la diffusion avec croissance de la quantite de matiere et son application a un probleme biologique, Bull. Univ. dEtat Moscou Ser. Intern. A, 1, 1 Li, 2005, Spreading speeds as slowest wave speeds for cooperative systems, Math. Biosci., 196, 82, 10.1016/j.mbs.2005.03.008 Liang, 2007, Asymptotic speeds of spread and traveling waves for monotone semiflows with applications, Comm. Pure Appl. Math., 60, 1, 10.1002/cpa.20154 Liang, 2006, Spreading speeds and traveling waves for periodic evolution systems, J. Differential Equations, 231, 57, 10.1016/j.jde.2006.04.010 Lui, 1989, Biological growth and spread modeled by systems of recursions, I. Mathematical theory, Math. Biosci., 93, 269, 10.1016/0025-5564(89)90026-6 Martin, 1976 Murray, 2002, Mathematical Biology, I and II, vol. 17 Nussbaum, 1981, Eigenvectors of nonlinear positive operator and the linear Krein–Rutman theorem, vol. 886, 309 Rass, 2003, Spatial Deterministic Epidemics, vol. 102 Shigesada, 1997 Shigesada, 1986, Traveling periodic waves in heterogeneous environments, Theor. Popul. Biol., 30, 143, 10.1016/0040-5809(86)90029-8 Vazquez, 2007, Porous medium flow in a tube: Traveling waves and KPP behavior, Commun. Contemp. Math., 9, 731, 10.1142/S0219199707002587 Vazquez, 2007 Volpert, 1994, Traveling Wave Solutions of Parabolic Systems, vol. 140 Weinberger, 1982, Long-time behavior of a class of biological models, SIAM J. Math. Anal., 13, 353, 10.1137/0513028 Weinberger, 2002, On spreading speeds and traveling waves for growth and migration models in a periodic habitat, J. Math. Biol., 45, 511, 10.1007/s00285-002-0169-3 Weinberger, 2008, Spreading speeds of spatially periodic integro-difference models for populations with non-monotone recruitment functions, J. Math. Biol., 57, 387, 10.1007/s00285-008-0168-0 P. Weng, X.-Q. Zhao, Spatial dynamics of a nonlocal and delayed population model in a periodic habitat, Discrete Contin. Dyn. Syst. Ser. A, in press Xin, 2000, Front propagation in heterogeneous media, SIAM Rev., 42, 161, 10.1137/S0036144599364296 Zhang, 2007, Asymptotic behavior of a reaction–diffusion model with a quiescent stage, Proc. R. Soc. A, 463, 1029, 10.1098/rspa.2006.1806 Zhao, 2003