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

Goro Akagi, Ryuji Kajikiya

Research output: Contribution to journalArticlepeer-review

2 Citations (Scopus)

Abstract

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.

Original languageEnglish
Pages (from-to)1155-1173
Number of pages19
JournalAnnales de l'Institut Henri Poincare (C) Analyse Non Lineaire
Volume31
Issue number6
DOIs
Publication statusPublished - 2014 Nov 1
Externally publishedYes

Keywords

  • Asymptotic profile
  • Fast diffusion equation
  • Semilinear elliptic equation
  • Stability analysis
  • Symmetry breaking

ASJC Scopus subject areas

  • Analysis
  • Mathematical Physics
  • Applied Mathematics

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