Blow-up and propagation of disturbances for fast diffusion equations

被引：3
|
作者：
Mainge, Paul-Emile [1 ]
机构：
[1] Univ Antilles Guyane, GRIMMAG, Dept Sci Interfacultaire, F-97230 Martinique, France
来源：
NONLINEAR ANALYSIS-THEORY METHODS & APPLICATIONS | 2008年 / 68卷 / 12期
关键词：
fast diffusion; finite blow-up time; Cauchy problem;
D O I：
10.1016/j.na.2007.04.030
中图分类号：
O29 [应用数学];
学科分类号：
070104 ;
摘要：
This paper is concerned with the Cauchy problem for the fast diffusion equation u(t) - Delta u(m) = alpha u(p1) in R-N (N >= 1), where m epsilon (0, 1), p(1) > 1 and alpha > 0. The initial condition u(0) is assumed to be continuous, nonnegative and bounded. Using a technique of subsolutions, we set up sufficient conditions on the initial value u(0) so that u(t, x) blows up in finite time, and we show how to get estimates on the profile of u(t, x) for small enough values of t > 0. (C) 2007 Elsevier Ltd. All rights reserved.
引用
收藏
页码：3913 / 3922
页数：10
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