  A phase field model proposed by G. Caginalp for the description of phase
changes in materials is under consideration. It is assumed that the medium is
located in a container with heat conductive walls that are not subjected to
phase changes. Therefore, the temperature variable is defined both in the
medium and wall regions, whereas the phase variable is only considered in the
medium part. The case of Lipschitz domains in two and three dimensions is
studied. We show that the temperature and phase variables are continuous in
time functions with values in $L^2$ and $H^1$, respectively, provided that the
initial values of them are from $L^2$ and $H^1$, respectively. Moreover,
continuous dependence of solutions on the initial data and boundary conditions
is proved.
