Symmetry and stability of asymptotic profiles for fast diffusion equations in annuli

被引：6

作者：

Akagi, Goro ^{[1
]}

Kajikiya, Ryuji ^{[2
]}

机构：

[1] Kobe Univ, Grad Sch Syst Informat, Nada Ku, Kobe, Hyogo 6578501, Japan

[2] Saga Univ, Fac Sci & Engn, Dept Math, Saga 8408502, Japan

来源：

ANNALES DE L INSTITUT HENRI POINCARE-ANALYSE NON LINEAIRE | 2014年 / 31卷 / 06期

关键词：

Fast diffusion equation; Semilinear elliptic equation; Asymptotic profile; Stability analysis; Symmetry breaking; SEMILINEAR ELLIPTIC-EQUATIONS; POSITIVE SOLUTIONS; UNIQUENESS; EXISTENCE; BEHAVIOR;

D O I：

10.1016/j.anihpc.2013.08.006

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

This paper is concerned with stability analysis of asymptotic profiles for (possibly sign-changing) solutions vanishing in finite time of the Cauchy-Dirichlet problems for fast diffusion equations in annuli. It is proved that the unique positive radial profile is not asymptotically stable, and moreover, it is unstable for the two-dimensional annulus. Furthermore, the method of stability analysis presented here will be also applied to exhibit symmetry breaking of least energy solutions. (C) 2013 Elsevier Masson SAS. All rights reserved.

引用

页码：1155 / 1173

页数：19

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