This paper considers the following quasilinear chemo-taxis system with indirect signal production and generalized logistic source{u_(t)=▽·(▽(u)▽u)-▽·(S(u)▽v)+μ(u-u^(Y)),x∈Ω,t>0 O=△v-v+w,x∈Ω,t&g...This paper considers the following quasilinear chemo-taxis system with indirect signal production and generalized logistic source{u_(t)=▽·(▽(u)▽u)-▽·(S(u)▽v)+μ(u-u^(Y)),x∈Ω,t>0 O=△v-v+w,x∈Ω,t>0 w_(t)=-δw+u,x∈Ω,t>0 under homogeneous Neumann boundary conditions in a smooth bounded domainΩ■R^(n)(n≥1),where the parametersμ,δ>0 andγ>1,the functions D(u)and S(u)are supposed to be smooth fulfilling D(u)≥C_(D)(u+1)^(-a)and S(u)≤C_(S)u(u+1)^(β-1)for all u≥0 with C D,α,β∈R and.It is proved that the corresponding initial-boundary value problem possesses a global bounded classical solution ifα+2β<γ-1.Moreover,ifμis suitably large,the asymptotic behavior and convergence rates are also been considered.展开更多
基金Supported by the Science and Technology Research Project of Chongqing Education Commission(KJQN202000618)。
文摘This paper considers the following quasilinear chemo-taxis system with indirect signal production and generalized logistic source{u_(t)=▽·(▽(u)▽u)-▽·(S(u)▽v)+μ(u-u^(Y)),x∈Ω,t>0 O=△v-v+w,x∈Ω,t>0 w_(t)=-δw+u,x∈Ω,t>0 under homogeneous Neumann boundary conditions in a smooth bounded domainΩ■R^(n)(n≥1),where the parametersμ,δ>0 andγ>1,the functions D(u)and S(u)are supposed to be smooth fulfilling D(u)≥C_(D)(u+1)^(-a)and S(u)≤C_(S)u(u+1)^(β-1)for all u≥0 with C D,α,β∈R and.It is proved that the corresponding initial-boundary value problem possesses a global bounded classical solution ifα+2β<γ-1.Moreover,ifμis suitably large,the asymptotic behavior and convergence rates are also been considered.
