DYNAMICS FOR A CHEMOTAXIS MODEL WITH GENERAL LOGISTIC DAMPING AND SIGNAL DEPENDENT MOTILITY  

作　　者：涂馨予 穆春来 邱蜀燕 张静 Xinyu TU;Chunlai MU;Shuyan QIU;Jing ZHANG(School of Mathematics and Statistics,Southwest University,Chongqing,400715,China;Department of Applied Mathematics,The Hong Kong Polytechnic University,Hung Hom,Hong Kong,China;College of Mathematics and Statistics,Chongqing University,Chongqing,401331,China;School of Sciences,Southwest Petroleum University,Chengdu,610500,China)

机构地区：[1]School of Mathematics and Statistics,Southwest University,Chongqing,400715,China [2]Department of Applied Mathematics,The Hong Kong Polytechnic University,Hung Hom,Hong Kong,China [3]College of Mathematics and Statistics,Chongqing University,Chongqing,401331,China [4]School of Sciences,Southwest Petroleum University,Chengdu,610500,China

出　　处：《Acta Mathematica Scientia》2024年第3期1046-1063,共18页数学物理学报（B辑英文版）

基　　金：supported by the NSFC(12301260);the Hong Kong Scholars Program(XJ2023002,2023-078);the Double First-Class Construction-Talent Introduction of Southwest University(SWU-KR22037);the Chongqing Post-Doctoral Fund for Staying in Chongqing(2022);partially supported by the NSFC(12271064,11971082);the Chongqing Talent Support Program(cstc2022ycjh-bgzxm0169);the Natural Science Foundation of Chongqing(cstc2021jcyj-msxmX1051);the Fundamental Research Funds for the Central Universities(2020CDJQY-Z001,2019CDJCYJ001);the Key Laboratory of Nonlinear Analysis and its Applications(Chongqing University);Ministry of Education;Chongqing Key Laboratory of Analytic Mathematics and Applications;supported by the NSFC(12301261);the Scientific Research Starting Project of SWPU(2021QHZ016);the Sichuan Science and Technology Program(2023NSFSC1365);the Nanchong Municipal Government-Universities Scientific Cooperation Project(SXHZ045);supported by the China Scholarship Council(202206050060);the Graduate Research and Innovation Foundation of Chongqing(CYB22044)。

摘　　要：In this paper,we consider the fully parabolic Chemotaxis system with the general logistic source{ut=Δ(γ(v)u)+λu-μu^(k),x∈Ω,t>0,vt=△v+wz,x∈Ω,t>0,wt=-wz,x∈Ω,t>0,zt=△z-z+u,x∈Ω,t>0 whereΩ⊂ℝn(n≥1)is a smooth and bounded domain,λ≥0,μ≥0,κ>1,and the motility function satisfies thatγ(v)∈C3([0,∞)),γ(v)>0,γ′(v)≤0 for all v≥0.Considering the Neumann boundary condition,we obtain the global boundedness of solutions if one of the following conditions holds:(i)λ=μ=0,1≤nλ3;(ii)λ>0,μ>0,combined withκ>1,1≤n≤3 or k>n+2/4,,n>3.Moreover,we prove that the solution (u, v, w, z) exponentially converges to the constant steady state ((λ/μ)1/k-1,∫Ωv0dx+∫Ωw0dx/|Ω|,0,(λ/μ)1/k-1).

关 键 词：CHEMOTAXIS signal-dependent motility logistic source boundedness asymptotic behavior 

分 类 号：O175[理学—数学]