Positive effects of repulsion on boundedness in a fully parabolic attraction-repulsion chemotaxis system with logistic source

摘要

In this paper we study the global boundedness of solutions to the fully parabolic attraction-repulsion chemotaxis system with logistic source: u(t) = Delta u - chi del . (u del v) + xi del . (u del w) + f(u), v(t) = Delta v - beta v + alpha u, w(t) = Delta w - delta w + gamma u, subject to homogeneous Neumann boundary conditions in a bounded and smooth domain Omega subset of R-n (n >= 1), where chi, alpha, xi,gamma, beta and delta are positive constants, and f: R -> R is a smooth function generalizing the logistic source f(s) = a - bs(theta) for all s >= 0 with a >= 0, b >= 0 and theta >= 1. It is shown that when the repulsion cancels the attraction (i.e. chi alpha= xi gamma)>the solution is globally bounded if n <= 3, or 0 > 0(n):= min{n+2/4, n root n(2)+6n+17-n(2)-3n+4/4} with n >= 2 Therefore; due to theinhibition of repulsion to the attraction, in any spatial dimension, the exponent theta is allowed to take values less than 2 such that the solution is uniformly bounded in time. (c) 2017 Elsevier Inc. All rights reserved.