Stability analysis of asymptotic profiles for sign-changing solutions to fast diffusion equations

Goro Akagi, Ryuji Kajikiya

Research output: Contribution to journalArticlepeer-review

7 Citations (Scopus)

Abstract

Every solution u = u(x, t) of the Cauchy-Dirichlet problem for the fast diffusion equation, ∂ t ({pipe}u{pipe}m-2 u) = Δu in Ω × (0, ∞) with a smooth bounded domain Ω of ℝN and 2 < m < 2*: = 2N/(N - 2)+, vanishes in finite time at a power rate. This paper is concerned with asymptotic profiles of sign-changing solutions and a stability analysis of the profiles. Our method of proof relies on a detailed analysis of a dynamical system on some surface in the usual energy space as well as energy method and variational method.

Original languageEnglish
Pages (from-to)559-587
Number of pages29
Journalmanuscripta mathematica
Volume141
Issue number3-4
DOIs
Publication statusPublished - 2013 Jul
Externally publishedYes

ASJC Scopus subject areas

  • Mathematics(all)

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