Mathematics Colloquium
3:30 p.m., Friday
Math 100
Professor F. den Hollander
Nijmegen University
Heat Conduction in Planar Domains
The goal of this talk is to give an overview of what
is known about the problem of heat conduction in planar
domains. After describing some of the history, which
goes back to the 1966 paper by Mark Kac entitled
``Can one hear the shape of a drum?'', I will discuss
several results that have been derived over the years,
focussing in particular on the time evolution of the
heat content of a planar domain whose boundary is kept
at constant temperature. Three types of boundary are
of interest:
 polygonal
 smooth
 fractal.
For the latter type certain fractal exponents naturally
show up, but it turns out in addition that the time
evolution is `irregular' in a sense that will be
explained.
Refreshments will be served in Math Annex Room 1115, 3:15 p.m.
