Traveling Wave Solutions for Two Species Competitive Chemotaxis Systems

Document Type

Article

Publication Date

7-2-2021

Publication Title

Nonlinear Analysis: Theory, Methods and Applications

Volume

212

First page number:

1

Last page number:

25

Abstract

In this paper, we consider two species chemotaxis systems with Lotka–Volterra competition reaction terms. Under appropriate conditions on the parameters in such a system, we establish the existence of traveling wave solutions of the system connecting two spatially homogeneous equilibrium solutions with wave speed greater than some critical number c∗. We also show the non-existence of such traveling waves with speed less than some critical number c0∗, which is independent of the chemotaxis. Moreover, under suitable hypotheses on the coefficients of the reaction terms, we obtain explicit range for the chemotaxis sensitivity coefficients ensuring c∗=c0∗, which implies that the minimum wave speed exists and is not affected by the chemoattractant.

Keywords

Chemotaxis-models; Competition system; Traveling waves

Disciplines

Applied Mathematics | Biostatistics

Language

English

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