Optimal estimate on life span for semilinear heat equations with non-rarefied sources at infinity

被引：1

作者：

You, Liting ^{[1
]}

Yin, Jingxue ^{[1
]}

Luo, Yong ^{[1
]}

机构：

[1] South China Normal Univ, Sch Math Sci, Guangzhou 510631, Peoples R China

来源：

JOURNAL OF DIFFERENTIAL EQUATIONS | 2024年 / 394卷

基金：

中国国家自然科学基金;

关键词：

Semilinear heat equation; Optimal; Life span; Blow-up; Non-rarefied; CAUCHY-PROBLEM; BEHAVIOR;

D O I：

10.1016/j.jde.2024.02.038

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

This paper is devoted to studying in R(n )x (0, T ) (n > 1) the Cauchy problem for a semilinear heat equation with source term f (x) non-rarefied at infinity, subjected to zero initial data. To such a problem, the novelty of this work lies in: (a) similar to no source case, non-rarefaction of f at infinity brings about its classical solution blowing up in a finite time T* > 0; (b) we derive the optimal upper and lower bound on the life span T*. This may throw some light on studies of life span. (c) 2024 Elsevier Inc. All rights reserved.

引用

页码：278 / 295

页数：18