Boundedness and asymptotic stability in a two-species chemotaxis-competition model with signal-dependent sensitivity

Abstract

This paper deals with the two-species chemotaxis-competition system (Iquestion Presented) where Ω is a bounded domain in ℝn with smooth boundary ∂Ω, n ∈ ℕ; h, Χi are functions satisfying some conditions. In the case that Χi(w) = Χi, Bai-Winkler [1] proved asymptotic behavior of solutions to the above system under some conditions which roughly mean largeness of μ1,μ2. The main purpose of this paper is to extend the previous method for obtaining asymptotic stability. As a result, the present paper improves the conditions assumed in [1], i.e., the ranges of μ1, μ2 are extended.