Polygonal heat conductors with a stationary hot spot

Rolando Magnanini, Shigeru Sakaguchi

Research output: Contribution to journalArticlepeer-review

4 Citations (Scopus)

Abstract

We consider a convex polygonal heat conductor whose inscribed circle touches every side of the conductor. Initially, the conductor has constant temperature and, at every time, the temperature of its boundary is kept at zero. The hot spot is the point at which temperature attains its maximum at each given time. It is proved that, if the hot spot is stationary, then the conductor must satisfy two geometric conditions. In particular, we prove that these geometric conditions yield some symmetries provided the conductor is either pentagonal or hexagonal.

Original languageEnglish
Pages (from-to)1-18
Number of pages18
JournalJournal d'Analyse Mathematique
Volume105
Issue number1
DOIs
Publication statusPublished - 2008 Jan
Externally publishedYes

ASJC Scopus subject areas

  • Analysis
  • Mathematics(all)

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