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Bistable wave fronts in a stage-structured reaction-diffusion model for a single species with distributed maturation delay. (English) Zbl 1444.35095

Summary: This paper is concerned with bistable wave fronts in a class of nonlocal reaction diffusion model for a single species with stage structure and distributed maturation delay. By choosing the strong and weak kernel functions to transform system with delays to a two- or three-dimensional system without any delays, the existence of traveling wave fronts is established by abstract results. Then we prove the asymptotic stability (up to translation) of bistable wave fronts and the uniqueness of wave speeds by spectral analysis and upper and lower solution technique, respectively. At last, we apply these results to a single species model with special nonlinearity.

MSC:

35K40 Second-order parabolic systems
34K10 Boundary value problems for functional-differential equations
35A18 Wave front sets in context of PDEs
35C07 Traveling wave solutions
35K57 Reaction-diffusion equations
35R20 Operator partial differential equations (= PDEs on finite-dimensional spaces for abstract space valued functions)
35Q92 PDEs in connection with biology, chemistry and other natural sciences
92D25 Population dynamics (general)
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References:

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