Elsevier

Nonlinear Analysis

Volume 212, November 2021, 112480
Nonlinear Analysis

Traveling wave solutions for two species competitive chemotaxis systems

https://doi.org/10.1016/j.na.2021.112480Get rights and content
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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.

MSC

35B35
35B40
35K57
35Q92
92C17

Keywords

Chemotaxis-models
Competition system
Traveling waves

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