首页|GLOBAL WEAK SOLUTIONS FOR AN ATTRACTION-REPULSION CHEMOTAXIS SYSTEM WITH p-LAPLACIAN DIFFUSION AND LOGISTIC SOURCE
GLOBAL WEAK SOLUTIONS FOR AN ATTRACTION-REPULSION CHEMOTAXIS SYSTEM WITH p-LAPLACIAN DIFFUSION AND LOGISTIC SOURCE
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This paper is concerned with the following attraction-repulsion chemotaxis sys-tem with p-Laplacian diffusion and logistic source:{ut=(▽).(|(▽)u|p-2(▽)u)-x(▽)·(u(▽)v)+ξ(▽)·(u▽w)+f(u),x ∈ Ω,t＞0,vt=△v-βv+αuk1,x ∈ Ω,t＞0,0=△w-δw+γuk2,x ∈ Ω,t＞0,u(x,0)=uo(x),v(x,0)=v0(x),w(x,0)=wo(x),x ∈ Ω.The system here is under a homogenous Neumann boundary condition in a bounded domainΩ C Rn(n ≥ 2),with x,ξ,α,β,γ,δ,k1,k2＞0,p ≥ 2.In addition,the function f is smooth and satisfies that f(s)≤ κ-μst for all s ≥ 0,with κ ∈ R,p＞0,1＞1.It is shown that(ⅰ)if l＞max{2k1,2k1n/2+n+1/p-1},then system possesses a global bounded weak solution and(ⅱ)ifk2＞max{2k1-1,2k1n/2+n+2-p/p-1}with l＞2,then system possesses a global bounded weak solution.
global weak solutionsattraction-repulsionp-Laplacianlogistic source
王晓闪、王忠谦、贾哲
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Department of Mathematics,Luoyang Normal University,Luoyang 471934,China
School of Mathematics Science,Jiangsu Second Normal University,Nanjing 210013,China
School of Mathematics and Statistics,Linyi University,Linyi 276005,China
National Natural Science Foundation of ChinaNational Natural Science Foundation of ChinaNatural Science Foundation of Shandong Province,ChinaScientific Research Foundation of Linyi University,China
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