[CvGmt News] Seminari di Calcolo delle Variazioni e Analisi Geometrica

[magnani at dm.unipi.it]

How to locate the hot spot in a heat conductor?
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Speaker: Lorenzo Brasco (Universita` di Napoli ''Federico II'')
Seminari di Calcolo delle Variazioni e Analisi Geometrica
13 Aprile 2011

   Dipartimento di Matematica - Sala Seminari - ore 17:00

   ABSTRACT: One considers the following physical situation: we have a
   heat conductor ''Omega'' having uniform temperature (say equal to 1, up
   to normalizations) at the initial time t=0. Then we ground it, i.e. we
   constantly keep its boundary at zero temperature, and we look at the
   evolution in time of its temperature, which we suppose to be ruled by
   the heat equation. What can be said about the location of the hot
   spots, i.e. the points where for each time the maximal temperature is
   attained? In this seminar, we illustrate two methods for estimating the
   location of these points, which are particularly useful when ''Omega''
   is a convex set: indeed in this case, one can ensure that at each time
   we just have a unique hot spot. These methods also apply to the
   location of some other important points (Santalo` point, maximum point
   of the first Dirichlet eigenfunction, etc.). These results are
   contained in a recent work joint with Rolando Magnanini and Paolo
   Salani (University of Florence).


You find this news in the cvgmt preprint server: http://cvgmt.sns.it/news/20110413/