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

页码：1761 / 1774

页数：14

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