Blow-up set for type i blowing up solutions for a semilinear heat equation

Yohei Fujishima, Kazuhiro Ishige

Research output: Contribution to journalArticlepeer-review

9 Citations (Scopus)

Abstract

Let u be a type I blowing up solution of the Cauchy-Dirichlet problem for a semilinear heat equation, { ∂tu = Δu + up, x ε Ω, t > 0, u(x, t) = 0, x ε ∂Ω, t > 0, u(x, 0) = φ(x), x ε Ω, where Ω is a (possibly unbounded) domain in RN, N≥1, and p>1. We prove that, if φ ε L (Ω)∩Lq(Ω) for some q ε [1, ∞ ), then the blow-up set of the solution u is bounded. Furthermore, we give a sufficient condition for type I blowing up solutions not to blow up on the boundary of the domain Ω. This enables us to prove that, if Ω is an annulus, then the radially symmetric solutions of (P) do not blow up on the boundary ∂Ω.

Original languageEnglish
Pages (from-to)231-247
Number of pages17
JournalAnnales de l'Institut Henri Poincare (C) Analyse Non Lineaire
Volume31
Issue number2
DOIs
Publication statusPublished - 2014 Jan 1

ASJC Scopus subject areas

  • Analysis
  • Mathematical Physics
  • Applied Mathematics

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