On heat conductors with a stationary hot spot

Rolando Magnanini, Shigeru Sakaguchi

Research output: Contribution to journalArticlepeer-review

11 Citations (Scopus)

Abstract

We consider a heat conductor having initial constant temperature and zero boundary temperature at every time. The hot spot is the point at which temperature attains its maximum at each given time. For convex conductors, if the hot spot does not move in time, we prove symmetry results for planar triangular and quadrangular conductors. Then, we examine the case of a general conductor and, by an asymptotic formula, we prove that, if there is a stationary critical point, not necessarily the hot spot, then the conductor must satisfy a geometric condition. In particular, we show that there is no stationary critical point inside planar non-convex quadrangular conductors.

Original languageEnglish
Pages (from-to)1-23
Number of pages23
JournalAnnali di Matematica Pura ed Applicata
Volume183
Issue number1
DOIs
Publication statusPublished - 2004 Mar 1
Externally publishedYes

Keywords

  • Convex bodies
  • Heat equation
  • Hot spots
  • Stationary critical point

ASJC Scopus subject areas

  • Applied Mathematics

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