Blow-up for degenerate parabolic equations with nonlocal source

被引：19

作者：

Chen, YP ^{[1
]}

Liu, QL ^{[1
]}

Xie, CH ^{[1
]}

机构：

[1] Nanjing Univ, Dept Math, Nanjing 210093, Peoples R China

来源：

PROCEEDINGS OF THE AMERICAN MATHEMATICAL SOCIETY | 2004年 / 132卷 / 01期

关键词：

degenerate nonlocal problem; classical solution; global existence; blow-up set;

D O I：

10.1090/S0002-9939-03-07090-4

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

This paper deals with the blow-up properties of the solution to the degenerate nonlinear reaction diffusion equation with nonlocal source x(q)u(t)- (x(gamma)u(x))(x) = integral(0)(a)u(p)dx in (0, a) x (0, T) subject to the homogeneous Dirichlet boundary conditions. The existence of a unique classical nonnegative solution is established and the sufficient conditions for the solution exists globally or blows up in finite time are obtained. Furthermore, it is proved that under certain conditions the blow-up set of the solution is the whole domain.

引用

页码：135 / 145

页数：11

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