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 41 条

[1]

Amann H., 2001, Rev R Acad Cien Serie A Mat, V95, P85

[2] Porous medium equation with absorption and a nonlinear boundary condition [J].

Andreu, F ;

Mazón, JM ;

Toledo, J ;

Rossi, JD .

NONLINEAR ANALYSIS-THEORY METHODS & APPLICATIONS, 2002, 49 (04) :541-563

[3]

[Anonymous], 1999, Acta Math. Univ. Comenian (N.S.)

[4]

[Anonymous], 1991, Acta Math. Univ. Comen.

[5] On boundedness of solutions of reaction-diffusion equations with nonlinear boundary conditions [J].

Arrieta, Jose M. .

PROCEEDINGS OF THE AMERICAN MATHEMATICAL SOCIETY, 2008, 136 (01) :151-160

[6]

Bidaut-Veron M.-F., 1998, Equations aux derivees partielles et applications, P189

[7] GLOBAL-SOLUTIONS OF SEMI-LINEAR HEAT-EQUATIONS [J].

CAZENAVE, T ;

LIONS, PL .

COMMUNICATIONS IN PARTIAL DIFFERENTIAL EQUATIONS, 1984, 9 (10) :955-978

[8] Existence of positive solutions of a semilinear elliptic equation in R+n with a nonlinear boundary condition [J].

Chipot, M ;

Chlebik, M ;

Fila, M ;

Shafrir, I .

JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS, 1998, 223 (02) :429-471

[9]

Chipot M., 2004, J DYN DIFFER EQU, V16, P91

[10]

Chipot M., 1996, Adv. Differ. Equ, V1, P91

← 1 2 3 4 5 →