Traveling wave solutions for two species competitive chemotaxis systems

2020/10/21 by Issa, T. B., Salako, R. B, Shen, W.
#35B35 #35B40 #35K57 #35Q92 #92C17 #Analysis of PDEs (math.AP) #FOS: Mathematics

paper · doi:10.48550/arxiv.2010.11335

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.

Related

• Traveling wave solutions for two species competitive chemotaxis systems
• Existence of Traveling wave solutions of parabolic-parabolic chemotaxis systems
• Two-species competition model with chemotaxis: well-posedness, stability and dynamics
• On the weakly competitive case in a two-species chemotaxis model
• Global existence and steady states of a two competing species Keller-Segel chemotaxis model