  We prove here well-posedness and convergence to equilibria for the solution
trajectories associated to a model for solidification of a liquid content of a
rigid container in a gravity field. We observe that the gravity effects, which
can be neglected without considerable changes of the process on finite time
intervals, have a substantial influence on the long time behavior of the
evolution system. Without gravity, we find a temperature interval, in which all
phase distributions with a prescribed total liquid contents are admissible
equilibria, while, under the influence of gravity, the only equilibrium
distribution in a connected container consists in two pure phases separated by
one plane interface perpendicular to the gravity force.
