HEAT EQUATION WITH A NONLINEAR BOUNDARY CONDITION AND UNIFORMLY LOCAL Lr SPACES

被引：21

作者：

Ishige, Kazuhiro ^{[1
]}

Sato, Ryuichi ^{[1
]}

机构：

[1] Tohoku Univ, Math Inst, Aoba Ku, Sendai, Miyagi 9808578, Japan

来源：

DISCRETE AND CONTINUOUS DYNAMICAL SYSTEMS | 2016年 / 36卷 / 05期

基金：

日本学术振兴会;

关键词：

Nonlinear boundary condition; heat equation; uniformly local L-r spaces; blow-up time; blow-up rate; BLOW-UP RATE; PARABOLIC EQUATIONS; GLOBAL EXISTENCE; CAUCHY-PROBLEM; TIME;

D O I：

10.3934/dcds.2016.36.2627

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

We establish the local existence and the uniqueness of solutions of the heat equation with a nonlinear boundary condition for the initial data in uniformly local L-r spaces. Furthermore, we study the sharp lower estimates of the blow-up time of the solutions with the initial data lambda psi as lambda -> 0 or lambda -> infinity and the lower blow-up estimates of the solutions.

引用

页码：2627 / 2652

页数：26

共 36 条

[11]

Chlebk M., 1999, Rend. Mat. Appl. (7) 19, V4, P449

[12]

Deng K., 1994, Acta Math. Univ. Comenian. (N.S.), V63, P169

[13] CONTINUITY OF WEAK SOLUTIONS TO A GENERAL POROUS-MEDIUM EQUATION [J].

DIBENEDETTO, E .

INDIANA UNIVERSITY MATHEMATICS JOURNAL, 1983, 32 (01) :83-118

[14]

DiBenedetto E., 1993, Degenerate parabolic equations, DOI [10.1007/978-1-4612-0895-2, DOI 10.1007/978-1-4612-0895-2]

[15]

Fernandez Bonder J., 2001, TSUKUBA J MATH, V25, P215

[16] THE BLOW-UP RATE FOR THE HEAT-EQUATION WITH A NONLINEAR BOUNDARY-CONDITION [J].

FILA, M ;

QUITTNER, P .

MATHEMATICAL METHODS IN THE APPLIED SCIENCES, 1991, 14 (03) :197-205

[17]

Fila M., 1989, COMMENT MATH U CAROL, V30, P479

[18] LOCAL EXISTENCE OF GENERAL NONLINEAR PARABOLIC-SYSTEMS [J].

FILO, J ;

KACUR, J .

NONLINEAR ANALYSIS-THEORY METHODS & APPLICATIONS, 1995, 24 (11) :1597-1618

[19] On critical Fujita exponents for heat equations with nonlinear flux conditions on the boundary [J].

Galaktionov, VA ;

Levine, HA .

ISRAEL JOURNAL OF MATHEMATICS, 1996, 94 :125-146

[20]

Giga MH, 2010, PROG NONLINEAR DIFFE, V79, P1, DOI 10.1007/978-0-8176-4651-6

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