DEAD-CORE RATES FOR THE POROUS MEDIUM EQUATION WITH A STRONG ABSORPTION

被引：7
|
作者：
Chen, Xinfu [1 ]
Guo, Jong-Shenq [2 ]
Hu, Bei [3 ]
机构：
[1] Univ Pittsburgh, Dept Math, Pittsburgh, PA 15260 USA
[2] Tamkang Univ, Dept Math, New Taipei City 25137, Taiwan
[3] Univ Notre Dame, Dept Appl & Computat Math & Stat, Notre Dame, IN 46556 USA
来源：
DISCRETE AND CONTINUOUS DYNAMICAL SYSTEMS-SERIES B | 2012年 / 17卷 / 06期
基金：
美国国家科学基金会;
关键词：
Dead-core rate; porous medium equation; strong absorption; HEAT-EQUATION;
D O I：
10.3934/dcdsb.2012.17.1761
中图分类号：
O29 [应用数学];
学科分类号：
070104 ;
摘要：
We study the dead-core rate for the solution of the porous medium equation with a strong absorption. It is known that solutions with certain class of initial data develop a dead-core in finite time. We prove that, unlike the cases of semilinear heat equation and fast diffusion equation, there are solutions with the self-similar dead-core rate. This result is based on the construction of a Lyapunov functional, some a priori estimates, and a delicate analysis of the associated re-scaled ordinary differential equation.
引用
收藏
页码：1761 / 1774
页数：14
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