Flow in a porous visco-elasto-plastic solid

−βθ div ut , has been derived and existence of global strong solutions in 3D for the isothermal case has been proved in [1]. Existence for the full system under suitable hypotheses is proved in [2]. The unknowns are u (displacement of the solid matrix), p (capillary pressure), and θ (absolute temperature). The system contains four hysteresis operators: The degenerate Preisach operator G describing pressure-saturation hysteresis, P describing elastoplastic hysteresis, and the associated dissipation operators DP and DG. The main challenge in the existence proof is related to the degeneracy of G which has been handled by means of a hysteretic version of Moser’s iterations. The permeability μ is assumed to depend only on the pressure. A more realistic case of saturation dependence has been considered [3, 4], but existence results have been obtained only if solid-liquid interaction is neglected and if additional time or space regularizing operators are involved.