Convergence rate of a quasilinear parabolic-elliptic chemotaxis system with logistic source

This paper deals with the quasilinear parabolic-elliptic chemotaxis system {u(t) = del.(d(u) del u) - del . (chi u Delta v) +mu u(1- u) x is an element of Omega, t > 0 0= del v - v_u, x is an element of Omega, t > 0 under homogeneous Neumann boundary conditions in a bounded domain Omega subset of R-n with smooth boundary, where x > 0 and mu> 0. D(u) is supposed to satisfy D(0) > 0, D(u) >= u(alpha) with alpha is an element of (0,1). When n >= 2, the convergence rate of the solution is investigated. (C) 2019 Elsevier Inc. All rights reserved.