BLOW-UP RATE OF SOLUTIONS OF PARABOLIC POBLEMS WITH NONLINEAR BOUNDARY CONDITIONS

被引：5

作者：

Quittner, Pavol ^{[1
]}

Souplet, Philippe ^{[2
]}

机构：

[1] Comenius Univ, Dept Appl Math & Stat, Bratislava 84248, Slovakia

[2] Univ Paris 13, CNRS, Lab Analyse Geometr & Applicat, UMR 7539, F-93430 Villetaneuse, France

来源：

DISCRETE AND CONTINUOUS DYNAMICAL SYSTEMS-SERIES S | 2012年 / 5卷 / 03期

关键词：

Parabolic; nonlinear boundary conditions; blow-up rate; a priori estimate; REACTION-DIFFUSION EQUATIONS; HEAT-EQUATIONS; POSITIVE SOLUTIONS; GLOBAL-SOLUTIONS; UNIVERSAL BOUNDS; THEOREMS; DECAY;

D O I：

10.3934/dcdss.2012.5.671

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

We review known and prove new results on blow-up rate of solutions of parabolic problems with nonlinear boundary conditions. We also compare these results and methods of their proofs with corresponding results and methods for the nonlinear heat equation.

引用

页码：671 / 681

页数：11

共 50 条

[1] Estimates on Blow-up Rate of Nonlinear Parabolic Systems with Nonlinear Boundary Conditions
LIU Wei-ling
[J]. Chinese Quarterly Journal of Mathematics, 2005, (04) : 401 - 405
[2] Blow-up rate for radially symmetric solutions of some parabolic equations with nonlinear boundary conditions
Harada, Junichi
Mihara, Kotaro
[J]. JOURNAL OF DIFFERENTIAL EQUATIONS, 2012, 253 (05) : 1647 - 1663
[3] Blow-up solutions and global solutions for nonlinear parabolic equations with mixed boundary conditions
Zhang H.
[J]. Journal of Applied Mathematics and Computing, 2010, 32 (2) : 535 - 545
[4] Blow-up of solutions for a class of quasilinear parabolic equations with nonlinear Boundary conditions
Zhao, Jun Ping
Wang, Lan Fang
[J]. JOURNAL OF INTERDISCIPLINARY MATHEMATICS, 2012, 15 (06) : 439 - 448
[5] On blow-up of solutions for a class of nonlinear parabolic equations with Neumann boundary conditions
Ding, JT
[J]. INDIAN JOURNAL OF PURE & APPLIED MATHEMATICS, 2003, 34 (02): : 265 - 275
[6] Global and blow-up solutions for nonlinear parabolic equations with Robin boundary conditions
Ding, Juntang
[J]. COMPUTERS & MATHEMATICS WITH APPLICATIONS, 2013, 65 (11) : 1808 - 1822
[7] Blow-up solutions for a class of nonlinear parabolic equations with Dirichlet boundary conditions
Ding, JT
[J]. NONLINEAR ANALYSIS-THEORY METHODS & APPLICATIONS, 2003, 52 (06) : 1645 - 1654
[8] BLOW-UP SOLUTIONS FOR A CLASS OF NONLINEAR PARABOLIC EQUATIONS WITH MIXED BOUNDARY CONDITIONS
DING Juntang LI Shengjia (School of Mathematical Sciences
[J]. Journal of Systems Science & Complexity, 2005, (02) : 265 - 276
[9] Blow-Up for a Class of Parabolic Equations with Nonlinear Boundary Conditions
Zhao, Leina
[J]. ADVANCES IN NEURAL NETWORKS - ISNN 2011, PT I, 2011, 6675 : 222 - 230
[10] GLOBAL EXISTENCE AND BLOW-UP OF SOLUTIONS FOR PARABOLIC SYSTEMS WITH NONLINEAR NONLOCAL BOUNDARY CONDITIONS
Sen, Zhou
Yang, Zuodong
[J]. ELECTRONIC JOURNAL OF DIFFERENTIAL EQUATIONS, 2013,

← 1 2 3 4 5 →