Stability and instability of group invariant asymptotic profiles for fast diffusion equations

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1 Citation (Scopus)

Abstract

This paper is concerned with group invariant solutions for fast diffusion equations in symmetric domains. First, it is proved that the group invariance of weak solutions is inherited from initial data. After briefly reviewing previous results on asymptotic profiles of vanishing solutions and their stability, the notions of stability and instability of group invariant profiles are introduced under a similarly invariant class of perturbations, and moreover, some stability criteria are exhibited and applied to symmetric domain (e.g., annulus) cases.

Original languageEnglish
Pages (from-to)1-16
Number of pages16
JournalSpringer INdAM Series
Volume2
DOIs
Publication statusPublished - 2013
Externally publishedYes

Keywords

  • Asymptotic profile
  • Fast diffusion equation
  • Group invariance
  • Stability

ASJC Scopus subject areas

  • Mathematics(all)

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