  This article is concerned with the solution of a time-dependent shape
identification problem. Specifically we consider the heat equation in a domain,
which contains a time-dependent inclusion of zero temperature. The objective is
to detect this inclusion from the given temperature and heat flux at the
exterior boundary of the domain. To this end, for a given temperature at the
exterior boundary, the mismatch of the Neumann data is minimized. This
time-dependent shape optimization problem is then solved by a gradient-based
optimization method. Numerical results are presented which validate the present
approach.
