Spreading speeds for monostable equations with nonlocal dispersal in space periodic habitats

Journal of Differential Equations - Tập 249 Số 4 - Trang 747-795 - 2010
Wenxian Shen1, Aijun Zhang1
1Department of Mathematics & Statistics, Auburn University, Auburn, AL 36849, USA.

Tóm tắt

Từ khóa


Tài liệu tham khảo

Aronson, 1975, Nonlinear diffusion in population genetics, combustion, and nerve pulse propagation, vol. 466, 5

Aronson, 1978, Multidimensional nonlinear diffusions arising in population genetics, Adv. Math., 30, 33, 10.1016/0001-8708(78)90130-5

Bates, 2007, Existence, uniqueness and stability of the stationary solution to a nonlocal evolution equation arising in population dispersal, J. Math. Anal. Appl., 332, 428, 10.1016/j.jmaa.2006.09.007

Bates, 2003, Traveling waves of bistable dynamics on a lattice, SIAM J. Math. Anal., 35, 520, 10.1137/S0036141000374002

Berestycki, 2005, The speed of propagation for KPP type problems, I. Periodic framework, J. Eur. Math. Soc. (JEMS), 7, 172, 10.4171/jems/26

Berestycki, 2010, The speed of propagation for KPP type problems, II. General domains, J. Amer. Math. Soc., 23, 1, 10.1090/S0894-0347-09-00633-X

Berestycki, 2005, Analysis of periodically fragmented environment model: II. Biological invasions and pulsating traveling fronts, J. Math. Pures Appl., 84, 1101, 10.1016/j.matpur.2004.10.006

Bürger, 1988, Perturbations of positive semigroups and applications to population genetics, Math. Z., 197, 259, 10.1007/BF01215194

Chen, 1997, Existence, uniqueness, and asymptotic stability of traveling waves in nonlocal evolution equations, Adv. Differential Equations, 2, 125, 10.57262/ade/1366809230

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

Chen, 2003, Uniqueness and existence of traveling waves for discrete quasilinear monostable dynamics, Math. Ann., 326, 123, 10.1007/s00208-003-0414-0

Chen, 2008, Traveling waves in discrete periodic media for bistable dynamics, Arch. Ration. Mech. Anal., 189, 189, 10.1007/s00205-007-0103-3

Chow, 1998, Traveling waves in lattice dynamical systems, J. Differential Equations, 149, 248, 10.1006/jdeq.1998.3478

2001

Coville, 2006, On uniqueness and monotonicity of solutions of non-local reaction diffusion equation, Ann. Mat. Pura Appl., 185, 461, 10.1007/s10231-005-0163-7

Coville, 2005, Propagation speed of travelling fronts in non local reaction–diffusion equations, Nonlinear Anal., 60, 797, 10.1016/j.na.2003.10.030

Coville, 2008, Existence and uniqueness of solutions to a nonlocal equation with monostable nonlinearity, SIAM J. Math. Anal., 39, 1693, 10.1137/060676854

Coville, 2008, Nonlocal anisotropic dispersal with monostable nonlinearity, J. Differential Equations, 244, 3080, 10.1016/j.jde.2007.11.002

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

Fisher, 1937, The wave of advance of advantageous genes, Ann. of Eugenics, 7, 335, 10.1111/j.1469-1809.1937.tb02153.x

Förster, 1998, Local spectral radii and Collatz–Wielandt numbers of monic operator polynomials with nonnegative coefficients, Linear Algebra Appl., 268, 41, 10.1016/S0024-3795(97)89323-8

Freidlin, 1979, On the propagation of concentration waves in periodic and random media, Soviet Math. Dokl., 20, 1282

Grinfeld, 2005, Non-local dispersal, Differential Integral Equations, 18, 1299, 10.57262/die/1356059743

Guo, 2006, Front propagation for discrete periodic monostable equations, Math. Ann., 335, 489, 10.1007/s00208-005-0729-0

Hamel, 2008, Qualitative properties of monostable pulsating fronts: Exponential decay and monotonicity, J. Math. Pures Appl., 89, 355, 10.1016/j.matpur.2007.12.005

Henry, 1981, Geometric Theory of Semilinear Parabolic Equations, vol. 840

G. Hetzer, W. Shen, A. Zhang, Effects of spatial variations and dispersal strategies on principal eigenvalues of dispersal operators and spreading speeds of monostable equations, preprint

Huang, 2009, Speeds of spread and propagation for KPP models in time almost and space periodic media, SIAM J. Appl. Dyn. Syst., 8, 790, 10.1137/080723259

Hudson, 1995, Existence of traveling waves for reaction diffusion equations of Fisher type in periodic media, 187

Hudson, 1994, Existence of traveling waves for a generalized discrete Fisher's equation, Comm. Appl. Nonlinear Anal., 1, 23

Hutson, 2006, Non-local dispersal and bistability, European J. Appl. Math., 17, 221, 10.1017/S0956792506006462

Hutson, 2003, The evolution of dispersal, J. Math. Biol., 47, 483, 10.1007/s00285-003-0210-1

Hutson, 2008, Spectral theory for nonlocal dispersal with periodic or almost-periodic time dependence, Rocky Mountain J. Math., 38, 1147, 10.1216/RMJ-2008-38-4-1147

Kametaka, 1976, On the nonlinear diffusion equation of Kolmogorov–Petrovskii–Piskunov type, Osaka J. Math., 13, 11

Kao, 2010, Random dispersal vs non-local dispersal, Discrete Contin. Dyn. Syst., 26, 551, 10.3934/dcds.2010.26.551

Kato, 1966

Kolmogorov, 1937, A study of the equation of diffusion with increase in the quantity of matter, and its application to a biological problem, Bjul. Moskovskogo Gos. Univ., 1, 1

Levermore, 1992, Multidimensional stability of traveling waves in a bistable reaction–diffusion equation. II, Comm. Partial Differential Equations, 17, 1901, 10.1080/03605309208820908

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, Math. Biosci., 93, 269, 10.1016/0025-5564(89)90026-6

Mallet-Paret, 1999, The Fredholm alternative for functional-differential equations of mixed type, J. Dynam. Differential Equations, 11, 1, 10.1023/A:1021889401235

Mallet-Paret, 1999, The global structure of traveling waves in spatially discrete dynamical systems, J. Dynam. Differential Equations, 11, 49, 10.1023/A:1021841618074

Nolen, 2005, Existence of KPP fronts in spatially–temporally periodic advection and variational principle for propagation speeds, Dyn. Partial Differ. Equ., 2, 1, 10.4310/DPDE.2005.v2.n1.a1

Nolen, 2005, Existence of KPP type fronts in space–time periodic shear flows and a study of minimal speeds based on variational principle, Discrete Contin. Dyn. Syst., 13, 1217, 10.3934/dcds.2005.13.1217

Pazy, 1983

Popovic, 2006, Rigorous asymptotic expansions for critical wave speeds in a family of scalar reaction–diffusion equations, J. Dynam. Differential Equations, 18, 103, 10.1007/s10884-005-9002-1

Ryzhik, 2007, KPP pulsating front speed-up by flows, Commun. Math. Sci., 5, 575, 10.4310/CMS.2007.v5.n3.a4

Sattinger, 1976, On the stability of waves of nonlinear parabolic systems, Adv. Math., 22, 312, 10.1016/0001-8708(76)90098-0

W. Shen, Variational principle for spatial spreading speeds and generalized propagating speeds in time almost and space periodic KPP models, Trans. Amer. Math. Soc., in press

Shen, 2009, Spreading and generalized propagating speeds of discrete KPP models in time varying environments, Front. Math. China, 4, 523, 10.1007/s11464-009-0032-6

Shen, 2007, Spectral theory for general nonautonomous/random dispersal evolution operators, J. Differential Equations, 235, 262, 10.1016/j.jde.2006.12.015

Uchiyama, 1978, The behavior of solutions of some nonlinear diffusion equations for large time, J. Math. Kyoto Univ., 18, 453, 10.1215/kjm/1250522506

Weinberger, 1982, Long-time behavior of a class of biology 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

Wu, 1997, Asymptotic and periodic boundary value problems of mixed FDEs and wave solutions of lattice differential equations, J. Differential Equations, 135, 315, 10.1006/jdeq.1996.3232

Xin, 1991, Existence and stability of traveling waves in periodic media governed by a bistable nonlinearity, J. Dynam. Differential Equations, 3, 541, 10.1007/BF01049099

Xin, 1992, Multidimensional stability of traveling waves in a bistable reaction–diffusion equation. I, Comm. Partial Differential Equations, 17, 1889, 10.1080/03605309208820907

Zinner, 1992, Existence of traveling wavefront solutions for the discrete Nagumo equation, J. Differential Equations, 96, 1, 10.1016/0022-0396(92)90142-A

Zinner, 1991, Stability of traveling wavefronts for the discrete Nagumo equation, SIAM J. Math. Anal., 22, 1016, 10.1137/0522066

Zinner, 1993, Traveling wavefronts for the discrete Fisher's equation, J. Differential Equations, 105, 46, 10.1006/jdeq.1993.1082