Blow-up, Concentration Phenomenon and Global Existence for the Keller-Segel Model in High Dimension

被引：52
|
作者：
Calvez, Vincent [1 ]
Corrias, Lucilla [2 ]
Ebde, Mohamed Abderrahman [3 ]
机构：
[1] Ecole Normale Super Lyon, CNRS, Unite Math Pures & Appl, UMR 5669, F-69364 Lyon 07, France
[2] Univ Evry Val Essonne, Dept Math, Evry, France
[3] Univ Paris 13, CNRS, Inst Galilee, Lab Anal Geometrie & Applicat,UMR 7539, F-93430 Villetaneuse, France
来源：
COMMUNICATIONS IN PARTIAL DIFFERENTIAL EQUATIONS | 2012年 / 37卷 / 04期
关键词：
Blow-up; Chemotaxis; Energy methods; Global weak solutions; Local weak solutions; Parabolic systems; TIME AGGREGATION; CHEMOTAXIS MODEL; DIFFUSION; SYSTEM; SOBOLEV; MASS;
D O I：
10.1080/03605302.2012.655824
中图分类号：
O29 [应用数学];
学科分类号：
070104 ;
摘要：
This article is devoted to the analysis of the classical Keller-Segel system over R-d, d >= 3. We describe as much as possible the dynamics of the system characterized by various criteria, both in the parabolic-elliptic case and in the fully parabolic case. The main results in the parabolic-elliptic case are: local existence without smallness assumption on the initial density and a quantified blow-up rate, global existence under an improved smallness condition and comparison of blow-up criteria. A new concentration phenomenon for the fully parabolic case is also given.
引用
收藏
页码：561 / 584
页数：24
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