Asymptotic Behavior in a Quasilinear Fully Parabolic Chemotaxis System with Indirect Signal Production and Logistic Source

• 作者: LI Dan LI Zhongping
• 来源期刊: 偏微分方程（英文版）
• 年，卷（期）: 2021,（2）
• 页码范围: 129-143
• 页数: 15页
• 分类号: O175.29
• 语种: 英文
• DOI: 10.4208/jpde.v34.n2.3

摘要

In this paper,we study the asymptotic behavior of solutions to a quasilinear fully parabolic chemotaxis system with indirect signal production and logistic source {ut=▽·(D(u)Vu)-▽·(S(u)▽v)+b-μuγ,x∈Ω,t＞0,vt=Δv-a1v+b1w,x∈Ω,t＞0,wt=Δw-a2w+b2u,x∈Ω,t＞0 under homogeneous Neumann boundary conditions in a smooth bounded domain Ω ? Rn(n≥1),where b≥0,γ≥1,a,≥1,,μ,bi＞0(i=1,2),D,S ∈ C2([0,∞))fulfilling D(s)≥a0(s+1)-α,0≤S(s)≤b0(s+1)β for all s≥0,where a0,b0＞0 and α,β ∈ IR are constants.The purpose of this paper is to prove that if b≥0 and μ＞0 sufficiently large,the globally bounded solution(u,v,w)with nonnegative initial data(u0,v0,w0)satisfies‖u(·,t)-(b/μ)1/γ‖L∞(Ω)+‖v(·,t)-b1b2/a1a2(b/μ)1/γ‖L∞(Ω)+‖w(·,t)-b2/a2(b/μ)1/γ‖L∞(Ω)→0 as t →∞.