On a fully parabolic chemotaxis system with Lotka-Volterra competitive kinetics

This paper is devoted to the following fully parabolic chemotaxis system with Lotka-Volterra competitive kinetics {u(t) = Delta u - chi(1)del.(u del w) + mu(1)u(1 - u - a(1)v), x is an element of Omega, t > 0, v(t) = Delta v - chi(2)del.(v del w) + mu(2)v(1 - v - a(2)u), x is an element of Omega, t > 0, w(t) =Delta w - lambda w + b(1)u + b(2)v, x is an element of Omega, t > 0, under homogeneous Neumann boundary conditions, where Omega subset of R-n is a bounded domain with smooth boundary. We mainly consider the global existence and boundedness of classical solutions in the three dimensional case, which extends and partially improves the results of Bai-Winkler (2016) [1], Xiang (2018) [25], as well as Lin-Mu-Wang (2015) [10], etc. (C) 2018 Elsevier Inc. All rights reserved.