Global solutions for a semilinear heat equation in the exterior domain of a compact set

Kazuhiro Ishige, Michinori Ishiwata

Research output: Contribution to journalArticlepeer-review

Abstract

Let u be a global in time solution of the Cauchy-Dirichlet problem for a semilinear heat equation, ∂ tu = Δu + u p; x ε ω t > 0, u = 0, x ε ∂ω t > 0, u(x, 0) = φ(x) ≥ 0; x ε ω where ∂ t = ∂/∂t, p > 1 + 2/N, N ≥ 3, ω is a smooth domain in R N, and φ ε L (ω). In this paper we give a suffcient condition for the solution u to behave like ||u(t)||L∞(R N) = O(t -1/(p-1)) as t → ∞, and give a classication of the large time behavior of the solution u.

Original languageEnglish
Pages (from-to)847-865
Number of pages19
JournalDiscrete and Continuous Dynamical Systems
Volume32
Issue number3
DOIs
Publication statusPublished - 2012 Mar

Keywords

  • Exterior domain
  • Global solutions.
  • Semilinear heat equation

ASJC Scopus subject areas

  • Analysis
  • Discrete Mathematics and Combinatorics
  • Applied Mathematics

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