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Periodic traveling waves in a reaction-diffusion model with chemotaxis and nonlocal delay effect. (English) Zbl 1397.35059

Summary: In this paper, we study the existence of periodic traveling wave solutions with large wave speed for a reaction-diffusion model with chemotaxis and nonlocal delay effect by applying the perturbation method. The proof relies on an abstract formulation of the wave profile as a solution of an operator equation in a certain Banach space, coupled with the Lyapunov-Schmidt reduction and the implicit function theorem.

MSC:

35C07 Traveling wave solutions
92C17 Cell movement (chemotaxis, etc.)
35K57 Reaction-diffusion equations
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