HEAT EQUATION WITH A NONLINEAR BOUNDARY CONDITION AND UNIFORMLY LOCAL Lr SPACES

被引：21

作者：

Ishige, Kazuhiro ^{[1
]}

Sato, Ryuichi ^{[1
]}

机构：

[1] Tohoku Univ, Math Inst, Aoba Ku, Sendai, Miyagi 9808578, Japan

来源：

DISCRETE AND CONTINUOUS DYNAMICAL SYSTEMS | 2016年 / 36卷 / 05期

基金：

日本学术振兴会;

关键词：

Nonlinear boundary condition; heat equation; uniformly local L-r spaces; blow-up time; blow-up rate; BLOW-UP RATE; PARABOLIC EQUATIONS; GLOBAL EXISTENCE; CAUCHY-PROBLEM; TIME;

D O I：

10.3934/dcds.2016.36.2627

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

We establish the local existence and the uniqueness of solutions of the heat equation with a nonlinear boundary condition for the initial data in uniformly local L-r spaces. Furthermore, we study the sharp lower estimates of the blow-up time of the solutions with the initial data lambda psi as lambda -> 0 or lambda -> infinity and the lower blow-up estimates of the solutions.

引用

页码：2627 / 2652

页数：26

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