Annali di Matematica Pura ed Applicata

, Volume 183, Issue 1, pp 1–23

On heat conductors with a stationary hot spot

Article

DOI: 10.1007/s10231-003-0077-1

Cite this article as:
Magnanini, R. & Sakaguchi, S. Ann. Mat. Pura Appl. IV. Ser. (2004) 183: 1. doi:10.1007/s10231-003-0077-1
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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.

Keywords

heat equation convex bodies hot spots stationary critical point 

Copyright information

© Springer-Verlag 2003

Authors and Affiliations

  1. 1.Dipartimento di Matematica U. DiniUniversità di FirenzeFirenzeItaly
  2. 2.Department of Mathematical Sciences, Faculty of ScienceEhime UniversityEhimeJapan

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