Existence and blow-up for a degenerate parabolic equation with nonlocal source

被引：12
|
作者：
Li, FC [1 ]
Xie, CH [1 ]
机构：
[1] Nanjing Univ, Dept Math, Nanjing 210093, Peoples R China
来源：
NONLINEAR ANALYSIS-THEORY METHODS & APPLICATIONS | 2003年 / 52卷 / 02期
关键词：
degenerate parabolic equation; nonlocal source; global existence; blow-up; blow-up rate;
D O I：
10.1016/S0362-546X(02)00119-0
中图分类号：
O29 [应用数学];
学科分类号：
070104 ;
摘要：
In this paper, we investigate the positive solution of nonlinear degenerate equation u(t) = u(p)(Deltau+au integral(Omega)u(q) dx) with Dirichlet boundary condition. Conditions on the existence of global and blow-up solution are given. Furthermore, it is proved that there exist two positive constants C-1, C-2 such that C-1(T* - t)(-1/(p+q)) less than or equal to max(xis an element of(Ω) over bar) u(x, t) less than or equal to C-2(T* - t)(-1/(p+q)). (C) 2002 Elsevier Science Ltd. All rights reserved.
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页码：523 / 534
页数：12
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