Analysis of a nonlinear coupled model of flow in deformable porous media

This work analyzes a variant of a model introduced by K.R. Rajagopal describing a flow through a deformable porous solid where the viscosity of the fluid and drag coefficient depend on the fluid’s pressure. The variant consists in truncating and regularizing the pressure in space by convolution and in time by convolution plus retardation. For this variant, a priori estimates and existence of solutions are established.