Blow-up for a nonlocal parabolic equation

被引：1

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.

引用

页码：3551 / 3562

页数：12

共 35 条

[1] [Anonymous], DIFFER INTEGRAL EQU
[2] THE THERMISTOR PROBLEM - EXISTENCE, SMOOTHNESS, UNIQUENESS, BLOWUP
ANTONTSEV, SN
CHIPOT, M
[J]. SIAM JOURNAL ON MATHEMATICAL ANALYSIS, 1994, 25 (04) : 1128 - 1156
[3] Bebernes J., 1997, Adv. Diff. Eq, V2, P927
[4] Cannon J.R., 2008, J. Integral Equ. Appl., V20, P243
[5] Cimatti G., 2002, Ann. Mat. Pura Appl, V181, P181, DOI [10.1007/s102310100034, DOI 10.1007/S102310100034]
[6] On a class of nonlocal elliptic problems via Galerkin method
Corrêa, FJSA
Filho, DCD
[J]. JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS, 2005, 310 (01) : 177 - 187
[7] Radial solutions for a nonlocal boundary value problem
Enguica, Ricardo
Sanchez, Luis
[J]. BOUNDARY VALUE PROBLEMS, 2006, 2006 (1)
[8] FIJALKOWSKI P, 2003, TOPOL METHOD NONL AN, V21, P293, DOI DOI 10.12775/TMNA.2003.017
[9] BLOW-UP OF POSITIVE SOLUTIONS OF SEMILINEAR HEAT-EQUATIONS
FRIEDMAN, A
MCLEOD, B
[J]. INDIANA UNIVERSITY MATHEMATICS JOURNAL, 1985, 34 (02) : 425 - 447
[10] Gomes J.M., 2005, Applicable Analysis, V84, P909

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