一类具局部化源的快扩散方程解的熄灭

吉林大学学报(理学版)

一类具局部化源的快扩散方程解的熄灭

孟繁慧¹, 高文杰²

1. 长春金融高等专科学校, 长春 130028; 2. 吉林大学数学学院, 长春 130012

收稿日期:2013-04-22 出版日期:2013-11-26 发布日期:2013-11-21
通讯作者: 高文杰 E-mail:wjgao@jlu.edu.cn

Extinction of Solutions to a Class of Fast Diffusion Equations with Localized Sources

MENG Fanhui¹, GAO Wenjie²

1. Changchun Finance College, Changchun 130028, China;2. College of Mathematics, Jilin University, Changchun 130012, China

Received:2013-04-22 Online:2013-11-26 Published:2013-11-21
Contact: GAO Wenjie E-mail:wjgao@jlu.edu.cn

摘要/Abstract

摘要：

研究一类具局部化源的快扩散方程解的熄灭性质. 通过分析非线性扩散项和非线性源项对解熄灭的影响并借助一些特殊构造的上下解, 得到了该问题解的临界熄灭指标. 结果表明: 当源项指标适当大时, 该问题的解对于适当小的初值在有限时刻熄灭; 当源项指标适当小时, 其最大解不熄灭.

关键词: 快扩散方程, 局部化源, 临界熄灭指标

Abstract:

This paper deals with the extinction properties of solutions to a class of fast diffusion equations coupled with localized sources. Analyzing the effect of the diffusion term and the source term on the extinction properties of solutions and constructing some proper sub and supersolutions, the authors obtained the critical extinction exponents of the problem. The results show that when the exponent of the source term is suitably large any solution of the problem vanishes in finite time for appropriately small initial data, while the maximal solution will not vanish at any finite time provided that the exponent of the source term is suitably small.

Key words: fast diffusion equation, localized source, critical extinction exponent

中图分类号:

O175.8

孟繁慧, 高文杰. 一类具局部化源的快扩散方程解的熄灭[J]. 吉林大学学报(理学版), 2013, 51(06): 1041-4045.

MENG Fanhui, GAO Wenjie. Extinction of Solutions to a Class of Fast Diffusion Equations with Localized Sources[J]. Journal of Jilin University Science Edition, 2013, 51(06): 1041-4045.