Solid liquid phase changes with different densities

In this paper we present a new thermodynamically consistent phase transition model describing the evolution of a liquid substance, e.g., water, in a rigid container Ω when we freeze the container. Since the density ̺2 of ice with volume fraction β2 , is lower than the density ̺1 of water with volume fraction β1 , experiments for instance the freezing of a glass bottle filled with water show that the water pressure increases up to the rupture of the bottle. When the container is not impermeable, freezing may produce a non-homogeneous material, for instance water ice or sorbet. Here we describe a general class of phase transition processes including this example as particular case. Moreover, we study the resulting nonlinear and singular PDE system from the analytical viewpoint recovering existence of a global (in time) weak solution and also uniqueness for some particular choices of the nonlinear functions involved.