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).
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)
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)。
