Traveling wave solutions for two species competitive chemotaxis systems. (November 2021)

• Record Type: Journal Article
• Authors: Issa, T.B.; Salako, R.B.; Shen, W.
• Is Part Of: Nonlinear analysis. Volume 212(2021)
• Publication Date: 2021-11
• Subjects: 35B35 -- 35B40 -- 35K57 -- 35Q92 -- 92C17; Chemotaxis-models -- Competition system -- Traveling waves; Mathematical analysis -- Periodicals; Functional analysis -- Periodicals; Nonlinear theories -- Periodicals; Analyse mathématique -- Périodiques; Analyse fonctionnelle -- Périodiques; Théories non linéaires -- Périodiques; Functional analysis; Mathematical analysis; Nonlinear theories; Periodicals; Electronic journals; 515.7248
• DOI: 10.1016/j.na.2021.112480
• Languages: English
• ISSNs: 0362-546X

Abstract

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 c 0 ∗, 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 ∗ = c 0 ∗, which implies that the minimum wave speed exists and is not affected by the chemoattractant.