On a Darcy-Stefan Problem arising in freezing and thawing of saturated porous media

A model with phase change for material convection in a saturated porous med ium with a frozen region is formulated as a Darcy-Stefan problem. We propos e a new generalized formulation for this Stefan-type problem with convectio n governed by Darcy's law. This approach, which is valid for irregular geom etries with irregular subregions, has the advantage of not requiring the sm oothness of the temperature, that restricted previous mathematical works to two-dimensional particular cases. We show existence of generalized solutio ns, passing to the limit in suitable approximated problems, which in princi ple can be solved numerically by the finite element method.