MODELING CAPILLARY HYSTERESIS IN UNSATURED POROUS MEDIA

This paper deals with the modeling of cyclic hysteresis phenomena for flows in unsaturated porous media, using a dynamic regularization process of Sobolev type. The addition of a kinematic regularizing term of third-order partial derivatives, depending on a strictly positive, small real parameter, enables us to capture the missing information of the ill-posed hysteresis phenomena via Rankine-Hugoniot and "entropy" inequalities. When this parameter tends to zero, an oriented hysteresis loop, corresponding to the realistic problem modeled, emerges from the flow of an associated auxiliary ordinary differential equation.