Critical exponents and blow-up rate for a nonlinear diffusion equation with logarithmic boundary flux

被引：7

作者：

Li, Zhongping ^{[1
,2
]}

Mu, Chunlai ^{[1
]}

机构：

[1] Chongqing Univ, Coll Math & Phys, Chongqing 400044, Peoples R China

[2] China W Normal Univ, Coll Math & Informat, Nanchong 637002, Peoples R China

来源：

NONLINEAR ANALYSIS-THEORY METHODS & APPLICATIONS | 2010年 / 73卷 / 04期

关键词：

Critical exponents; Blow-up; Blow-up rate; Nonlinear diffusion equation; Logarithmic boundary flux; POROUS-MEDIUM EQUATION; CRITICAL FUJITA EXPONENTS; LINEAR HEAT-EQUATIONS; PARABOLIC EQUATIONS; INSTABILITY; STABILITY; THEOREMS;

D O I：

10.1016/j.na.2010.04.011

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

In this paper, we establish the critical global existence exponent and the critical Fujita exponent for the nonlinear diffusion equation u(t) = (log(sigma) (1 + u)u(x))(x), in R(+) x (0, +infinity), subject to a logarithmic boundary flux - log(sigma) (1 + u)u(x) (0, t) = (1 + u) log(p) (1 + u) (0, t), t is an element of (0, +infinity), furthermore give the blow-up rate for the nonglobal solutions. (C) 2010 Elsevier Ltd. All rights reserved.

引用

页码：933 / 939

页数：7

共 23 条

[1]

ANDERSON JR, 1993, J DIFFER EQUATIONS, V104, P386, DOI 10.1006/jdeq.1993.1078

[2] STABILITY AND INSTABILITY FOR SOLUTIONS OF THE CONVECTIVE POROUS-MEDIUM EQUATION WITH A NONLINEAR FORCING AT THE BOUNDARY .1. [J].

ANDERSON, JR .

JOURNAL OF DIFFERENTIAL EQUATIONS, 1993, 104 (02) :361-385

[3]

[Anonymous], 1996, 2 ORDER PARABOLIC DI, DOI DOI 10.1142/3302

[4]

ARONSON DG, 1986, LECT NOTES MATH, V1224, P1

[5] Blow-up and global solutions for nonlinear reaction-diffusion equations with Neumann boundary conditions [J].

Ding, Juntang ;

Li, Shengjia .

NONLINEAR ANALYSIS-THEORY METHODS & APPLICATIONS, 2008, 68 (03) :507-514

[6] Blow-up with logarithmic nonlinearities [J].

Ferreira, Raul ;

de Pablo, Arturo ;

Rossi, Julio D. .

JOURNAL OF DIFFERENTIAL EQUATIONS, 2007, 240 (01) :196-215

[7]

Fujita H., 1966, J. Fac. Sci. Univ. Tokyo Sec. 1A Math, V16, P105

[8]

Galaktionov V. A., 1980, Soviet Physics - Doklady, V25, P458

[9]

Galaktionov VA, 2002, DISCRETE CONT DYN-A, V8, P399

[10] Blow-up for quasilinear heat equations described by means of nonlinear Hamilton-Jacobi equations [J].

Galaktionov, VA ;

Vazquez, JL .

JOURNAL OF DIFFERENTIAL EQUATIONS, 1996, 127 (01) :1-40

← 1 2 3 →