Global existence and asymptotic stability of solutions to a two-species chemotaxis system with any chemical diffusion

This paper deals with the two-species chemotaxis system {u(t) = Delta u - del.(u(chi 1)(w)del w) + mu(1)u(1-u) in Omega x (0, infinity), v(t) = del u - del.(v(chi 1)(w)del w) + mu(2)v(1-u) in Omega x (0, infinity), w(t) = d Delta w + h(u,v,w) in Omega x (0, infinity), where Omega is a bounded domain in R-n with smooth boundary partial derivative Omega, n is an element of N; h, chi(i) are functions satisfying some conditions. Negreanu Tello (2014, 2015) [12,13] proved global existence and asymptotic behavior of solutions to the above system when 0 <= d < 1. The main purpose of the present paper is to remove the restriction of 0 <= d <1. (C) 2016 Elsevier Inc. All rights reserved.