带Logistic源的奇异趋化系统解的整体存在性  

Global Existence of Classical Solutions to a Singular Chemotaxis System with Logistic Source

作　　者：王娇 

机构地区：[1]辽宁师范大学数学学院,辽宁 大连

出　　处：《理论数学》2024年第10期219-225,共7页Pure Mathematics

摘　　要：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.

关 键 词：趋化 奇异灵敏度 Logistic源 整体存在 

分 类 号：O17[理学—数学]