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On spreading speeds and traveling waves for growth and migration models in a periodic habitat. (English) Zbl 1058.92036
Summary: It is shown that the methods previously used by the author [SIAM J. Math. Anal. 13, 353–396 (1982; Zbl 0529.92010)] and by R. Lui [Math. Biosci. 93, 269–295 (1989; Zbl 0706.92014)] to obtain asymptotic spreading results and sometimes the existence of traveling waves for a discrete-time recursion with a translation invariant order preserving operator can be extended to a recursion with a periodic order preserving operator. The operator can be taken to be the time-one map of a continuous time reaction-diffusion model, or it can be a more general model of time evolution in population genetics or population ecology in a periodic habitat. Methods of estimating the speeds of spreading in various directions will also be presented.

MSC:
92D15 Problems related to evolution
92D40 Ecology
35K55 Nonlinear parabolic equations
47N60 Applications of operator theory in chemistry and life sciences
35K57 Reaction-diffusion equations
35B40 Asymptotic behavior of solutions to PDEs
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