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Traveling wavefronts in a reaction-diffusion model with chemotaxis and nonlocal delay effect. (English) Zbl 1415.35080

Summary: This paper is devoted to the study of traveling wavefronts of 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 Fredholm theory and the Banach contraction mapping principle. This result is illustrated by an application to the chemotaxis-diffusion-growth model with the logistic source and a single delay effect.

MSC:

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