Blow-up directions at space infinity for solutions of semilinear heat equations

被引：36

作者：

Giga, Yoshikazu ^{[1
]}

Umeda, Noriaki ^{[1
]}

机构：

[1] Univ Tokyo, Grad Sch Math Sci, Meguro Ku, 3-8-1,Komaba, Tokyo 1538914, Japan

来源：

BOLETIM SOCIEDADE PARANAENSE DE MATEMATICA | 2005年 / 23卷 / 1-2期

基金：

日本学术振兴会;

关键词：

nonlinear heat equation; blow-up at space infinity; blow-up direction;

D O I：

10.5269/bspm.v23i1-2.7450

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

A blowing up solution of the semilinear heat equation ut = Delta u+ f (u) with f satisfying lim inf f (u)/u(p) > 0 for some p > 1 is considered when initial data u(0) satisfies u(0) <= M, u(0) not equivalent to M and lim(m) (>infinity) inf(x)is an element of B-m u(0)(x) = M with sequence of ball {B-m} whose radius diverging to infinity. It is shown that the solution blows up only at space infinity. A notion of blow-up direction is introduced. A characterization for blow-up direction is also established.

引用

页码：9 / 28

页数：20

共 13 条

[1] Fast blow-up mechanisms for sign-changing solutions of a semilinear parabolic equation with critical nonlinearity [J].