We investigate the location of the (unique) hot spot in a convex heat conductor with uniform initial temperature and with boundary grounded at zero temperature. We present two methods to locate the hot spot: the first is based on ideas related to the Alexandrov-Bakelmann-Pucci maximum principle and Monge-Amp\` ere equations; the second relies on Alexandrov's reflection principle. We then show how such a problem can be simplified in case the conductor is a polyhedron. Finally, we present some numerical computations.
The location of the hot spot in a grounded convex conductor
BRASCO, Lorenzo;
2011
Abstract
We investigate the location of the (unique) hot spot in a convex heat conductor with uniform initial temperature and with boundary grounded at zero temperature. We present two methods to locate the hot spot: the first is based on ideas related to the Alexandrov-Bakelmann-Pucci maximum principle and Monge-Amp\` ere equations; the second relies on Alexandrov's reflection principle. We then show how such a problem can be simplified in case the conductor is a polyhedron. Finally, we present some numerical computations.File in questo prodotto:
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