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.

引用

页码：437 / 446

页数：10

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