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

Abstract

This paper deals with the quasilinear parabolic-elliptic chemotaxis system{ut=∇⋅(D(u)∇u)−∇⋅(χu∇v)+μu(1−u),x∈Ω,t>0,0=Δv−v+u,x∈Ω,t>0, under homogeneous Neumann boundary conditions in a bounded domain Ω⊂Rn with smooth boundary, where χ>0 and μ>0. D(u) is supposed to satisfyD(0)>0,D(u)≥uαwithα∈(0,1). When n≥2, the convergence rate of the solution is investigated.