Hysteresis in Filtration through Porous Media

Abstract

We study an evolution problem for filtration through porous media, accounting for hysteresis in the saturation versus pressure constitutive relation. We provide a weak formulation of the problem, assuming that the memory effect in the constitutive relation consists not only of a rate-independent component but also of a rate-dependent one. We prove an existence result, which also applies to the case where the hysteresis operator is of Preisach-type.