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

作     者：LI Dan LI Zhongping LI Dan;LI Zhongping

作者机构：College of Mathematic and InformationChina West Normal UniversityNanchong 637009China 

出 版 物：《Journal of Partial Differential Equations》 (偏微分方程（英文版）)

年 卷 期：2021年第34卷第2期

页      面：129-143页

核心收录：

学科分类：07[理学] 070104[理学-应用数学] 0701[理学-数学] 

基　　金：The paper is supported by the National Science Foundation of China(11301419) the Meritocracy Research Funds of China West Normal University[17YC382] 

主　　题：Chemotaxis system indirect signal logistic source asymptotic behavior 

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)■u)-■·(S(u)■v)+b-μur,x∈Ω,t0,vt=Δv+a1v+b1w,x∈Ω,t0,wt=Δw-a2w+b2u,x∈Ω,t0 under homogeneous Neumann boundary conditions in a smooth bounded domainΩ■R^(N)(N≥1),where b≥0,γ≥1,ai≥1,μ,bi0(i=1,2,D,S∈C^(2)([0,∞))fulfilling D(S)≥a0(s+1)^(-a),0≤S(s)≤b0(s+1)^(β)for all s≥0,where a0,b00 and a,β≤R are *** pur purpose of this paper is to prove that if b≥0 andμ0 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)→0ast→∞.