On a Viscoelastoplastic Porous Medium Problem with Nonlinear Interaction
Chiara Gavioli, Pavel Krejčı́ · SIAM Journal on Mathematical Analysis · 2021
A PDE system consisting of the mechanical equilibrium and mass balance equations for displacement and capillary pressure as a model for fluid diffusion in a partially saturated viscoelastoplastic porous solid with a nonlinear solid-liquid interaction and a degenerate pressure-saturation function is shown to admit a solution under appropriate assumptions on the constitutive behavior. If the diffusion coefficient is constant, then the solution is unique and depends continuously on the data.