Existence and nonexistence of solutions for the heat equation with a superlinear source term

被引：35

作者：

Fujishima, Yohei ^{[1
]}

Ioku, Norisuke ^{[2
]}

机构：

[1] Shizuoka Univ, Fac Engn, Dept Math & Syst Engn, 3-5-1 Johoku, Hamamatsu, Shizuoka 4338561, Japan

[2] Ehime Univ, Grad Sch Sci & Engn, Matsuyama, Ehime 7908577, Japan

来源：

JOURNAL DE MATHEMATIQUES PURES ET APPLIQUEES | 2018年 / 118卷

关键词：

Nonlinear heat equation; Scale invariance; Singular initial data; Existence and nonexistence; LINEAR PARABOLIC EQUATIONS; BLOW-UP; GLOBAL-SOLUTIONS; LOCAL EXISTENCE; WELL-POSEDNESS; CAUCHY-PROBLEM; UNIQUENESS; SUPERSOLUTIONS; NONUNIQUENESS;

D O I：

10.1016/j.matpur.2018.08.001

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

We develop a classification theory for the existence and non-existence of local in time solutions for initial value problems for nonlinear heat equations. By focusing on some quasi-scaling property and its invariant integral, we reveal the explicit threshold integrability of initial data that classifies the existence and nonexistence of solutions. Typical nonlinear terms, for instance polynomial type, exponential type and their sums, products and compositions can be treated as applications. (C) 2018 Elsevier Masson SAS. All rights reserved.

引用

页码：128 / 158

页数：31

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