本文研究一类在齐次Neumann边界条件下的具有奇异灵敏度和Logistic源的抛物–抛物趋化系统:ut=Δu−χ∇⋅(uv∇v)+ru−μuk,vt=Δv−v+u,其中Ω⊂ℝn为光滑有界凸域,μ,χ>0,r∈ℝ。证明了当于k>1及χ≤4n时,系统存在唯一的整体古典解。Th...本文研究一类在齐次Neumann边界条件下的具有奇异灵敏度和Logistic源的抛物–抛物趋化系统:ut=Δu−χ∇⋅(uv∇v)+ru−μuk,vt=Δv−v+u,其中Ω⊂ℝn为光滑有界凸域,μ,χ>0,r∈ℝ。证明了当于k>1及χ≤4n时,系统存在唯一的整体古典解。This paper investigates a class of parabolic chemotaxis systems with singular sensitivity and Logistic sources under homogeneous Neumann boundary conditions: ut=Δu−χ∇⋅(uv∇v)+ru−μuk, vt=Δv−v+u, where Ω⊂ℝnis a smooth bounded convex domain, μ,χ>0, r∈ℝ. It is proved that for k>1with χ≤4n, the system admits a unique global classical solution.展开更多
文摘本文研究一类在齐次Neumann边界条件下的具有奇异灵敏度和Logistic源的抛物–抛物趋化系统:ut=Δu−χ∇⋅(uv∇v)+ru−μuk,vt=Δv−v+u,其中Ω⊂ℝn为光滑有界凸域,μ,χ>0,r∈ℝ。证明了当于k>1及χ≤4n时,系统存在唯一的整体古典解。This paper investigates a class of parabolic chemotaxis systems with singular sensitivity and Logistic sources under homogeneous Neumann boundary conditions: ut=Δu−χ∇⋅(uv∇v)+ru−μuk, vt=Δv−v+u, where Ω⊂ℝnis a smooth bounded convex domain, μ,χ>0, r∈ℝ. It is proved that for k>1with χ≤4n, the system admits a unique global classical solution.
