ASYMPTOTIC BEHAVIOR OF SINGULAR SOLUTIONS FOR A SEMILINEAR PARABOLIC EQUATION

被引：8

作者：

Sato, Shota ^{[2
]}

Yanagida, Eiji ^{[1
]}

机构：

[1] Tokyo Inst Technol, Dept Math, Meguro Ku, Tokyo 1528551, Japan

[2] Tohoku Univ, Math Inst, Sendai, Miyagi 9808578, Japan

来源：

DISCRETE AND CONTINUOUS DYNAMICAL SYSTEMS | 2012年 / 32卷 / 11期

基金：

日本学术振兴会;

关键词：

Semilinear parabolic equation; singular solution; convergence to a steady state; critical exponent; RADIAL HEAT EQUATION; POLYNOMIALS; TRANSFORMS;

D O I：

10.3934/dcds.2012.32.4027

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

We consider the Cauchy problem for a parabolic partial differential equation with a power nonlinearity. It is known that in some range of parameters, this equation has a family of singular steady states with ordered structure. Our concern in this paper is the existence of time-dependent singular solutions and their asymptotic behavior. In particular, we prove the convergence of solutions to singular steady states. The method of proofs is based on the analysis of a related linear parabolic equation with a singular coefficient and the comparison principle.

引用

页码：4027 / 4043

页数：17

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