Location of blow-up set for a semilinear parabolic equation with large diffusion

Kazuhiro Ishige, Noriko Mizoguchi

Research output: Contribution to journalArticlepeer-review

11 Citations (Scopus)

Abstract

This paper is concerned with {ut = DΔu + up in Ω × (0, TD), (P) ∂u/∂v (x, t) = 0 on ∂Ω × (0, TD), u (x, 0) = φ(x) ≥ 0 in Ω, where Ω is a bounded smooth domain in RN, TD > 0, D > 0, and p > 1 with (N-2) p ≤ N+2. Let P2 be the projection from L2(Ω) onto the second Neumann eigenspace. We prove that, if P2φ ≢ 0 in Ω and D is sufficiently large, the solution u of (P) blows up only near the set M ∪ ∂Ω, where script M sign = {x ∈ Ω̄: (P2φ)(x) = maxy∈Ω̄(P2φ)(y)}.

Original languageEnglish
Pages (from-to)487-511
Number of pages25
JournalMathematische Annalen
Volume327
Issue number3
DOIs
Publication statusPublished - 2003 Nov 1

ASJC Scopus subject areas

  • Mathematics(all)

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