EXISTENCE AND ASYMPTOTIC BEHAVIOR OF SOLUTIONS TO A SINGULAR PARABOLIC EQUATION

被引：0

作者：

夏莉 ^{[1
]}

李敬娜 ^{[2
]}

姚正安 ^{[3
]}

机构：

[1] Department of Mathematics,Shenzhen University

[2] Department of Mathematics,Jinan University

[3] Department of Mathematics,Sun Yat-Sen University

来源：

Acta Mathematica Scientia | 2012年 / 32卷 / 05期

关键词：

existence; singular parabolic equation; asymptotic behavior;

D O I：

暂无

中图分类号：

O175.26 [抛物型方程];

学科分类号：

070104 ;

摘要：

In this paper,we study the initial-boundary value problem for a class of singular parabolic equations.Under some conditions,we obtain the existence and asymptotic behavior of solutions to the problem by parabolic regularization method and the sub-super solutions method.As a byproduct,we prove the existence of solutions to some problems with gradient terms,which blow up on the boundary.

引用

页码：1875 / 1882

页数：8

共 7 条

[1]

CONTROLLABILITY FOR A PARABOLIC EQUATION WITH A NONLINEAR TERM INVOLVING THE STATE AND THE GRADIENT[J]. 许友军,刘振海. Acta Mathematica Scientia. 2010(05)

[2] A one-dimensional nonlinear heat equation with a singular term [J].

Zhou, Wenshu ;

Lei, Peidong .

JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS, 2010, 368 (02) :711-726

[3] Single-Point Gradient Blow-up on the Boundary for Diffusive Hamilton-Jacobi Equations in Planar Domains [J].

Li Yuxiang ;

Souplet, Philippe .

COMMUNICATIONS IN MATHEMATICAL PHYSICS, 2010, 293 (02) :499-517

[4]

Existence, uniqueness and asymptotic behavior of solutions for a singular parabolic equation[J] . Li Xia,Zheng’an Yao. Journal of Mathematical Analysis and Applications . 2009 (1)

[5]

Regularity and nonuniqueness results for parabolic problems arising in some physical models, having natural growth in the gradient[J] . Boumediene Abdellaoui,Andrea Dall’Aglio,Ireneo Peral. Journal de mathématiques pures et appliquées . 2008 (3)

[6] Nonuniqueness in the quenching problem [J].

Winkler, Michael .

MATHEMATISCHE ANNALEN, 2007, 339 (03) :559-597

[7]

Blowup in diffusion equations: A survey[J] . Catherine Bandle,Hermann Brunner. Journal of Computational and Applied Mathematics . 1998 (1)

← 1 →