Global Existence and Boundedness for the Attraction-repulsion Keller-Segel Model with Volume Filling Effect  

作　　者：Jian DENG 

机构地区：[1]School of Mathematical Sciences,South China Normal University,Guangzhou 510631,China

出　　处：《Acta Mathematicae Applicatae Sinica》2025年第2期513-524,共12页应用数学学报(英文版)

基　　金：supported by National Natural Science Foundation of China(12271186,11871230).

摘　　要：This paper is concerned with the attraction-repulsion Keller-Segel model with volume filling effect.We consider this problem in a bounded domainΩ■R^(3) under zero-flux boundary condition,and it is shown that the volume filling effect will prevent overcrowding behavior,and no blow up phenomenon happen.In fact,we show that for any initial datum,the problem admits a unique global-in-time classical solution,which is bounded uniformly.Previous findings for the chemotaxis model with volume filling effect were derived under the assumption 0≤u_(0)(x)≤1 withρ(x,t)≡1.However,when the maximum size of the aggregate is not a constant but rather a functionρ(x,t),ensuring the boundedness of the solutions becomes significantly challenging.This introduces a fundamental difficulty into the analysis.

关 键 词：classical solutions global boundedness attraction-repulsion volume filling effect 

分 类 号：O175.2[理学—数学]