Global existence, nonexistence and asymptotic behavior of solutions for the Cauchy problem of semilinear heat equations

被引：31

作者：

Liu Yacheng ^{[1
]}

Xu Runzhang ^{[1
]}

Yu Tao ^{[1
]}

机构：

[1] Harbin Engn Univ, Coll Sci, Harbin 150001, Peoples R China

来源：

NONLINEAR ANALYSIS-THEORY METHODS & APPLICATIONS | 2008年 / 68卷 / 11期

基金：

中国国家自然科学基金;

关键词：

semilinear heat equation; Cauchy problem; global existence; blowup; asymptotic behavior;

D O I：

10.1016/j.na.2007.03.029

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

In this paper, we study the Cauchy problem of semilinear heat equations. By introducing a family of potential wells, we first prove the invariance of some sets and isolating solutions. Then we obtain a threshold result for the global existence and nonexistence of solutions. Finally we discuss the asymptotic behavior of the solution. (C) 2007 Elsevier Ltd. All rights reserved.

引用

页码：3332 / 3348

页数：17

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