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Propagation dynamics of a nonlocal dispersal Fisher-KPP equation in a time-periodic shifting habitat. (English) Zbl 1428.35174

Summary: This paper is devoted to the study of the propagation dynamics of a nonlocal dispersal Fisher-KPP equation in a time-periodic shifting habitat. We first show that this equation admits a periodic forced wave with the speed at which the habitat is shifting by using the monotone iteration method combined with a pair of generalized super- and sub-solutions. Then we establish the nonexistence, uniqueness and global exponential stability of periodic forced waves by applying the sliding technique and the comparison argument. Finally, we obtain the spreading properties for a large class of solutions.

MSC:

35K57 Reaction-diffusion equations
35C07 Traveling wave solutions
35B40 Asymptotic behavior of solutions to PDEs
35Q92 PDEs in connection with biology, chemistry and other natural sciences
92D25 Population dynamics (general)
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