On homogenized equations of filtration in two domains with common boundary

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 Lamé constants and different microstructures, and of a viscous incompressible porous fluid. Under various assumptions on the data of the problem, we derive homogenized models of filtration of an incompressible weakly viscous fluid in two distinct elastic or absolutely rigid porous media with common boundary.