Blow-up for a nonlocal parabolic equation

被引：2
作者：
Liang Fei [1 ,2 ]
Li Yuxiang [1 ]
机构：
[1] Southeast Univ, Dept Math, Nanjing 210096, Peoples R China
[2] An Hui Sci & Technol Univ, Dept Math, Feng Yang 233100, Peoples R China
来源：
NONLINEAR ANALYSIS-THEORY METHODS & APPLICATIONS | 2009年 / 71卷 / 7-8期
基金：
中国国家自然科学基金;
关键词：
Nonlocal parabolic problem; Asymptotic behavior; Blow-up; THERMISTOR PROBLEM; DIFFUSION-EQUATIONS; BOUNDARY-BEHAVIOR; TIME; EXISTENCE;
D O I：
10.1016/j.na.2009.02.020
中图分类号：
O29 [应用数学];
学科分类号：
070104 ;
摘要：
In this paper, we consider the blow-up properties of the radial solutions of the nonlocal parabolic equation u(t) = Delta u + lambda u(alpha)/(integral(B1)(u + 1)(-alpha)dx)(p), x is an element of B-1, t > 0, with homogeneous Dirichlet boundary condition, where lambda, p > 0, 0 < alpha <= 1. The criteria for the solutions to blow-up in finite time is given. It is proved that the blow-up is global and uniform for 0 < alpha < 1, global and nonuniform for alpha = 1. The blow-up rate of vertical bar u vertical bar(infinity) is also determined. (C) 2009 Elsevier Ltd. All rights reserved.
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页码：3551 / 3562
页数：12
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