Boundedness of global solutions of a supercritical parabolic equation

被引：15

作者：

Chen, Xinfu ^{[2
]}

Fila, Marek ^{[3
]}

Guo, Jong-Shenq ^{[1
]}

机构：

[1] Natl Taiwan Normal Univ, Dept Math, Taipei 116, Taiwan

[2] Comenius Univ, Dept Appl Math & Stat, Bratislava 84248, Slovakia

[3] Univ Pittsburgh, Dept Math, Pittsburgh, PA 15260 USA

来源：

NONLINEAR ANALYSIS-THEORY METHODS & APPLICATIONS | 2008年 / 68卷 / 03期

基金：

美国国家科学基金会;

关键词：

global solutions; supercritical parabolic equation; SEMILINEAR HEAT-EQUATION; REACTION-DIFFUSION EQUATIONS; POSITIVE SOLUTIONS; BLOWUP;

D O I：

10.1016/j.na.2006.11.023

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

We study radially symmetric classical solutions of the Dirichlet problem for a heat equation with a supercritical nonlinear Source. We give a sufficient condition under which blow-up in infinite time cannot Occur. This condition involves only the growth rate of the source term at infinity. We do not need the homogeneity property which played a key role in previous proofs of similar results. We also establish the NOW-Up rate for a class Of Solutions which blow tip in finite time. (c) 2007 Published by Elsevier Ltd.

引用

页码：621 / 628

页数：8

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