Finite time blow-up for a one-dimensional quasilinear parabolic-parabolic chemotaxis system

被引：89
|
作者：
Cieslak, Tomasz [2 ]
Laurencot, Philippe [1 ]
机构：
[1] Univ Toulouse, Inst Math Toulouse, CNRS, UMR 5219, F-31062 Toulouse 9, France
[2] Warsaw Univ, Inst Appl Math, PL-02097 Warsaw, Poland
来源：
ANNALES DE L INSTITUT HENRI POINCARE-ANALYSE NON LINEAIRE | 2010年 / 27卷 / 01期
关键词：
DIFFUSION; EXISTENCE; MODEL;
D O I：
10.1016/j.anihpc.2009.11.016
中图分类号：
O29 [应用数学];
学科分类号：
070104 ;
摘要：
Finite time blow-up is shown to occur for solutions to a one-dimensional quasilinear parabolic-parabolic chemotaxis system as soon as the mean value of the initial condition exceeds some threshold value. The proof combines a novel identity of virial type with the boundedness from below of the Liapunov functional associated to the system, the latter being peculiar to the one-dimensional setting. (C) 2009 Elsevier Masson SAS. All rights reserved.
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页码：437 / 446
页数：10
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