Subcritical nonlinear heat equation

被引：3

作者：

Hayashi, Nakao ^{[1
]}

Kaikina, Elena I.

Naumkin, Pavel I.

机构：

[1] Osaka Univ, Grad Sch Sci, Dept Math, Toyonaka, Osaka 5600043, Japan

[2] Inst Matemat, Morelia 58089, Michoacan, Mexico

来源：

JOURNAL OF DIFFERENTIAL EQUATIONS | 2007年 / 238卷 / 02期

关键词：

D O I：

10.1016/j.jde.2007.04.007

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

We study asymptotic behavior in time of small solutions to nonlinear heat equations in subcritical case. We find a new family of self-similar solutions which change a sign. We show that solutions are stable in the neighborhood of these self-similar solutions. (c) 2007 Elsevier Inc. All rights reserved.

引用

收藏

页码：366 / 380

页数：15

相关论文

共 8 条

[1] LARGE TIME BEHAVIOR OF SOLUTIONS OF A DISSIPATIVE SEMILINEAR HEAT-EQUATION [J].

ESCOBEDO, M ;

KAVIAN, O ;

MATANO, H .

COMMUNICATIONS IN PARTIAL DIFFERENTIAL EQUATIONS, 1995, 20 (7-8) :1427-1452

[2]

Escobedo M., 1997, HOUSTON J MATH, V13, P39

[3]

FUJITA H, 1966, J FAC SCI U TOKYO 1, V13, P109

[4] LARGE TIME BEHAVIOR OF THE SOLUTIONS OF A SEMILINEAR PARABOLIC EQUATION IN RN [J].

GMIRA, A ;

VERON, L .

JOURNAL OF DIFFERENTIAL EQUATIONS, 1984, 53 (02) :258-276

[5] NONEXISTENCE OF GLOBAL SOLUTIONS OF SOME SEMILINEAR PARABOLIC DIFFERENTIAL EQUATIONS [J].

HAYAKAWA, K .

PROCEEDINGS OF THE JAPAN ACADEMY, 1973, 49 (07) :503-505

[6] Large time behaviour of solutions to the dissipative nonlinear Schrodinger equation [J].

Hayashi, N ;

Kaikina, EI ;

Naumkin, PI .

PROCEEDINGS OF THE ROYAL SOCIETY OF EDINBURGH SECTION A-MATHEMATICS, 2000, 130 :1029-1043

[7] Landau-Ginzburg type equations in the subcritical case [J].

Hayashi, N ;

Kaikina, EI ;

Naumkin, PI .

COMMUNICATIONS IN CONTEMPORARY MATHEMATICS, 2003, 5 (01) :127-145

[8] GROWING UP PROBLEM FOR SEMILINEAR HEAT EQUATIONS [J].

KOBAYASHI, K ;

SIRAO, T ;

TANAKA, H .

JOURNAL OF THE MATHEMATICAL SOCIETY OF JAPAN, 1977, 29 (03) :407-424