Boundedness of global solutions of a porous medium equation with a localized source

被引：12

作者：

Chen, YP ^{[1
]}

Liu, QL

Gao, HJ

机构：

[1] Yancheng Normal Inst, Dept Math, Yancheng 224002, Jiangsu, Peoples R China

[2] Nanjing Normal Univ, Dept Math, Nanjing 210097, Jiangsu, Peoples R China

来源：

NONLINEAR ANALYSIS-THEORY METHODS & APPLICATIONS | 2006年 / 64卷 / 10期

关键词：

porous medium equation; localized source; global existence; finite time blow-up; uniform boundedness;

D O I：

10.1016/j.na.2005.08.004

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

In this paper a localized porous medium equation u(t) = u(r) (Delta u + af (u(x(0), t))) is considered. It is shown that under certain conditions solutions of the above equation blow up in finite time for large a or large initial data while there exist global positive solutions to the above equation for small a or small initial data. Moreover, it is also shown that all global positive solutions of the above equation are uniformly bounded, and this differs from that of a porous medium equation with a local source. (c) 2005 Elsevier Ltd. All rights reserved.

引用

页码：2168 / 2182

页数：15

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