On the Fujita exponent for a semilinear heat equation with a potential term

Kazuhiro Ishige

Research output: Contribution to journalArticlepeer-review

11 Citations (Scopus)

Abstract

We consider the existence and nonexistence of positive global solutions for the Cauchy problem,{(∂t u = Δ u - V (x) u + up, in RN × (0, ∞),; u (x, 0) = φ{symbol} (x) ≥ 0, in RN,) where p > 1 and V behaves like ω | x |-2 (1 + o (1)) with ω > 0, as | x | → ∞. In this paper we determine the so-called Fujita exponent p* for this Cauchy problem. Furthermore, for the critical case p = p*, we prove that the Cauchy problem has no global positive solutions.

Original languageEnglish
Pages (from-to)231-237
Number of pages7
JournalJournal of Mathematical Analysis and Applications
Volume344
Issue number1
DOIs
Publication statusPublished - 2008 Aug 1

Keywords

  • Blow-up problem
  • Fujita exponent
  • Semilinear heat equation

ASJC Scopus subject areas

  • Analysis
  • Applied Mathematics

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