When does the heat equation have a solution with a sequence of similar level sets?

Tatsuki Kawakami, Shigeru Sakaguchi

Research output: Contribution to journalArticlepeer-review

Abstract

In this paper, we consider an overdetermined Cauchy problem for the heat equation. We prove that if the problem has a non-trivial nonnegative solution with a certain sequence of similar level sets, then the solution must be radially symmetric.

Original languageEnglish
Pages (from-to)1595-1605
Number of pages11
JournalAnnali di Matematica Pura ed Applicata
Volume194
Issue number6
DOIs
Publication statusPublished - 2014 Jun 15

Keywords

  • Heat equation
  • Overdetermined Cauchy problem
  • Similar level sets

ASJC Scopus subject areas

  • Applied Mathematics

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