  In the present paper, a continuum model is introduced for fluid flow in a
deformable porous medium, where the fluid may undergo phase transitions.
Typically, such problems arise in modeling liquid-solid phase transformations
in groundwater flows. The system of equations is derived here from the
conservation principles for mass, momentum, and energy and from the
Clausius-Duhem inequality for entropy. It couples the evolution of the
displacement in the matrix material, of the capillary pressure, of the absolute
temperature, and of the phase fraction. Mathematical results are proved under
the additional hypothesis that inertia effects and shear stresses can be
neglected. For the resulting highly nonlinear system of two PDEs, one ODE and
one ordinary differential inclusion with natural initial and boundary
conditions, existence of global in time solutions is proved by means of cut-off
techniques and suitable Moser-type estimates.
