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.

In this paper we prove the finite model property and decidability of a family of pretrasitive modal logics of finite height. We construct special partitions (filtrations) of pretransitive frames of finite height, which implies the finite model property and decidability of their modal logics.