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 language | English |
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Pages (from-to) | 1-23 |
Number of pages | 23 |
Journal | Annali di Matematica Pura ed Applicata |
Volume | 183 |
Issue number | 1 |
DOIs | |
Publication status | Published - 2004 Mar 1 |
Externally published | Yes |
Keywords
- Convex bodies
- Heat equation
- Hot spots
- Stationary critical point
ASJC Scopus subject areas
- Applied Mathematics