BOUNDEDNESS OF THE HIGHER-DIMENSIONAL QUASILINEAR CHEMOTAXIS SYSTEM WITH GENERALIZED LOGISTIC SOURCE

【摘要】 This article considers the following higher-dimensional quasilinear parabolicparabolic-ODE chemotaxis system with generalized Logistic source and homogeneous Neumann boundary conditions■in a bounded domain??Rⁿ（n≥2） with smooth boundary??, where the diffusion coefficient D（u） and the chemotactic sensitivity function S（u） are supposed to satisfy D（u）≥M1 （u+1）^-α and S（u）≤M2（u+1）^β, respectively, where M₁, M₂> 0 andα,β∈R. Moreover, the logistic source f （u） is supposed to satisfy f （u）≤a-μu^γ with μ> 0,γ≥1, and a≥0. As α+2β<γ-1+2γ/n, we show that the solution of the above chemotaxis system with sufficiently smooth nonnegative initial data is uniformly bounded.更多还原

【Abstract】 This article considers the following higher-dimensional quasilinear parabolicparabolic-ODE chemotaxis system with generalized Logistic source and homogeneous Neumann boundary conditions ■in a bounded domain??Rⁿ（n≥2） with smooth boundary??, where the diffusion coefficient D（u） and the chemotactic sensitivity function S（u） are supposed to satisfy D（u）≥M1 （u+1）^-α and S（u）≤M2（u+1）^β, respectively, where M₁, M₂> 0 andα,β∈R. Moreover, the logistic source f （u） is supposed to satisfy f （u）≤a-μu^γ with μ> 0,γ≥1, and a≥0. As α+2β<γ-1+2γ/n, we show that the solution of the above chemotaxis system with sufficiently smooth nonnegative initial data is uniformly bounded.更多还原