Samenvatting:
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?'', several results will
be described 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 that the time evolution is `irregular' in a sense that will be explained
in
the talk.