Blow-up and global solutions for nonlinear reaction-diffusion equations with Neumann boundary conditions

被引：12

作者：

Ding, Juntang ^{[1
]}

Li, Shengjia ^{[1
]}

机构：

[1] Shanxi Univ, Sch Math Sci, Taiyuan 030006, Shanxi, Peoples R China

来源：

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

基金：

中国国家自然科学基金;

关键词：

nonlinear reaction-diffusion equations; blow-up solutions; global solutions;

D O I：

10.1016/j.na.2006.11.016

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

The type of problem under consideration is [GRAPHICS] where D subset of R-N is a bounded domain with smooth boundary partial derivative D, N >= 2. It is proved that if beta - 1 > sigma >= alpha >= 0, the positive solution u(x, 1) blows up globally in (D) over bar, whereas if 0 <= beta <= sigma <= alpha-1, the positive solution u(x, t) is global solution. Furthermore, an upper bound of the "blow-up time", an upper estimate of the "blow-up rate", and an upper estimate of the global solutions are given. (c) 2006 Elsevier Ltd. All rights reserved.

引用

页码：507 / 514

页数：8

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