Hot spots for the heat equation with a rapidly decaying negative potential

Kazuhiro Ishige, Y. Kabeya

Research output: Contribution to journalArticle

6 Citations (Scopus)

Abstract

We consider the Cauchy problem of the heat equation with a radially symmetric, negative potential -V which behaves like V (r) = O(r-k) as r → ∞, for some k > 2, and study the relation between the large-time behavior of hot spots of the solutions and the behavior of the potential at the space infinity. In particular, we prove that the hot spots tend to the space infinity as t → ∞ and how their rates depend on whether V ({norm of matrix} ̇ {norm of matrix}) ε L1(RN) or not.

Original languageEnglish
Pages (from-to)643-662
Number of pages20
JournalAdvances in Differential Equations
Volume14
Issue number7-8
Publication statusPublished - 2009 Dec 1

ASJC Scopus subject areas

  • Analysis
  • Applied Mathematics

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