On homogenized equations of filtration in two domains with common boundary

Abstract

We consider an initial-boundary value problem describing the process of filtration of a weakly viscous fluid in two distinct porous media with common boundary. We prove, at the microscopic level, the existence and uniqueness of a generalized solution of the problem on the joint motion of two incompressible elastic porous (poroelastic) bodies with distinct Lam’e constants and different microstructures, and of a viscous incompressible porous fluid