On the Dependence of the Critical Exponent of the Nonlinear Heat Equation on the Initial Function

被引：4

作者：

Pokhozhaev, S. I. ^{[1
]}

机构：

[1] VA Steklov Math Inst, Moscow 117333, Russia

来源：

DIFFERENTIAL EQUATIONS | 2011年 / 47卷 / 07期

基金：

俄罗斯基础研究基金会;

关键词：

Cauchy Problem; Critical Exponent; Initial Function; Nonnegative Solution; Nonlinear Heat Equation;

D O I：

10.1134/S0012266111070044

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

We establish the dependence of the critical exponent of the nonlinear heat equation on the initial function and derive an estimate for the blow-up time of the solution of this problem depending on the nonlinearity exponent and the initial function.

引用

页码：955 / 962

页数：8