Studying the Darcy–Stefan problem on phase transition in a saturated porous soil

The Cauchy problem for the Darcy–Stefan model, which describes the process of freezing (thawing) of a saturated porous soil with allowance for liquid-phase filtration, is considered. The model includes the Darcy law, the equation of liquid-phase incompressibility, the equation of absence of solid-phase motion, the equation of energy balance in the porous soil-saturating continuous medium system, and also the Stefan condition and the condition of continuity of the normal components of the velocity field at the interface boundary. The existence of generalized solutions of the problem satisfying an additional condition of entropy nondecreasing in a thermomechanical system (i.e., the second law of thermodynamics) is proved by the method of the kinetic equation.