Large time behavior of solutions to a quasilinear attraction-repulsion chemotaxis system with logistic source

摘要

This paper studies the quasilinear attraction-repulsion chemotaxis system with a logistic source u(t) = del . (D(u)del u) - V . (Phi(u)del v) + del . (psi(u)del w) f(u), tau(1)v(t) = Delta v alpha u - beta v, tau(2)w(t) = Delta w + gamma u - delta w, under homogeneous Neumann boundary conditions in a bounded domain Omega subset of R-N (N >= 1), where tau(1), tau(2) is an element of {0, 1}, D, Phi, psi is an element of C-2 ([0, + infinity)) nonnegative with D(s) >= (s+ 1)(p) for s >= 0, Phi(s) <= chi s(q), xi s(r) <= psi(s) <= zeta s(r) for s >= s(0) > 0, f (s) <= mu s(1 - s(k)) for s > 0, f(0) >= 0. In a previous paper of the authors (Tian et al., 2016), the criteria for global boundedness of solutions were established for the case of tau(2) = 0, depending on the interaction among the multi-nonlinear mechanisms (diffusion, attraction, repulsion and source) in the model. This paper continuously determines the global boundedness conditions for the case of tau(2) = 1. In particular, we obtain the large time behavior of the globally bounded solutions for the situation of D(s) = (s+ 1)(p), Phi(s) = chi s(q), psi(s)= xi s(tau), f(s) = mu s(1 - s), s >= 0 with p = 2(q - 1) = 2(r - 1) >= 0, tau(1), tau(2) is an element of {0, 1}. (C) 2020 Elsevier Ltd. All rights reserved.