Blow-up of solutions to the Patlak-Keller-Segel equation in dimension ν ≥ 2

被引：3

作者：

Chen, Li ^{[1
]}

Siedentop, Heinz ^{[2
]}

机构：

[1] Univ Mannheim, Math Inst, A5 6, D-68131 Mannheim, Germany

[2] Ludwig Maximilians Univ Munchen, Math Inst, Theresienstr 39, D-80333 Munich, Germany

来源：

APPLIED MATHEMATICS LETTERS | 2017年 / 74卷

关键词：

Patlak-Keller-Segel equation; Blow-up; Higher dimension; CRITICAL MASS; MODEL; CHEMOTAXIS; IONIZATION; SYSTEM;

D O I：

10.1016/j.aml.2017.05.006

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

We prove a blow-up criterion for the solutions to the v-dimensional Patlak-Keller-Segel equation in the whole space. The condition is new in dimension three and higher. In dimension two it is exactly Dolbeault's and Perthame's blow-up condition, i.e., blow-up occurs if total mass exceeds 8 pi. (C) 2017 Elsevier Ltd. All rights reserved.

引用

页码：102 / 107

页数：6

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