Freezing of a porous medium with water supply coupled Stefan problem (Q1071187)

The aim of the paper is to build a model of a wet porous medium (e.g. a water saturated soil) which is freezing. Both thermal and hydraulic aspects are taken into account. The domain \(\Omega\) is divided into three time-dependent parts: The unfrozen part \(\Omega_ 1(t)\), the frozen part \(\Omega_ 2(t)\) and a zone \(\Omega_ 3(t)\) with the phase change temperature. They are separated by free surfaces. Physical equations and variational formulation of the problem are derived. It is shown that some slightly different sets than \(\Omega_ i(t)\) are more convenient to describe the problem and that the notion of free surface is not suitable. Existence theorems and a maximum principle are proven.