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

共 50 条

[1] Finite-time blow-up in the higher-dimensional parabolic-parabolic Keller-Segel system
Winkler, Michael
JOURNAL DE MATHEMATIQUES PURES ET APPLIQUEES, 2013, 100 (05): : 748 - 767
[2] BLOW-UP IN FINITE OR INFINITE TIME FOR QUASILINEAR DEGENERATE KELLER-SEGEL SYSTEMS OF PARABOLIC-PARABOLIC TYPE
Ishida, Sachiko
Yokota, Tomomi
DISCRETE AND CONTINUOUS DYNAMICAL SYSTEMS-SERIES B, 2013, 18 (10): : 2569 - 2596
[3] Finite-time blow-up for quasilinear degenerate Keller-Segel systems of parabolic-parabolic type
Hashira, Takahiro
Ishida, Sachiko
Yokota, Tomomi
JOURNAL OF DIFFERENTIAL EQUATIONS, 2018, 264 (10) : 6459 - 6485
[4] Finite-time blow-up in quasilinear parabolic-elliptic chemotaxis system with nonlinear signal production
Li, Yan
JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS, 2019, 480 (01)
[5] Finite-time blow-up in the higher dimensional parabolic-parabolic-ODE minimal chemotaxis-haptotaxis system
Rani, Poonam
Tyagi, Jagmohan
JOURNAL OF DIFFERENTIAL EQUATIONS, 2025, 423 : 133 - 160
[6] Boundedness and finite-time blow-up in a quasilinear parabolic-elliptic-elliptic attraction-repulsion chemotaxis system
Chiyo, Yutaro
Yokota, Tomomi
ZEITSCHRIFT FUR ANGEWANDTE MATHEMATIK UND PHYSIK, 2022, 73 (02):
[7] Blow-up behavior of solutions to a degenerate parabolic-parabolic Keller-Segel system
Ishige, Kazuhiro
Laurencot, Philippe
Mizoguchi, Noriko
MATHEMATISCHE ANNALEN, 2017, 367 (1-2) : 461 - 499
[8] Finite time blow-up in the higher dimensional parabolic-elliptic-ODE minimal chemotaxis-haptotaxis system
Xiang, Tian
JOURNAL OF DIFFERENTIAL EQUATIONS, 2022, 336 : 44 - 72
[9] Exact Traveling Wave Solutions of One-Dimensional Parabolic-Parabolic Models of Chemotaxis
Shubina, M., V
RUSSIAN JOURNAL OF MATHEMATICAL PHYSICS, 2018, 25 (03) : 383 - 395
[10] Finite-time blow-up in a higher-dimensional quasilinear parabolic-elliptic chemotaxis system with space dependent logistic source
Yang, Yuzhu
Li, Zhongping
JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS, 2021, 504 (02)

← 1 2 3 4 5 →