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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.

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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