  We propose here a model for solidification of a liquid contents of an elastic
bottle in a freezer. The main goal is to explain the occurrence of high
stresses inside the bottle. As a by-product, we derive a formula for the
undercooling coefficient in terms of the elasticity constants, latent heat, and
the phase expansion coefficient. We investigate the well-posedness of the
three-dimensional model: we prove the existence and uniqueness of a solution
for the corresponding initial-boundary value problem which couples a PDE with
an integrodifferential equation and an ordinary differential inclusion ruling
the evolution of the phase parameter. Finally, we prove some results on the
long time behavior of solutions.
