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

被引：2
|
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.
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页码：102 / 107
页数：6
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