Homogenization of a single phase flow through a porous medium in a thin layer

The paper deals with homogenization of stationary and non-stationary high contrast periodic double porosity type problem stated in a porous medium containing a 2D or 3D thin layer. We consider two different types of high contrast medium. The medium of the first type is characterized by the asymptotically vanishing volume fraction of fractures (highly permeable part). The medium of the second type has uniformly positive volume fraction of fracture part. In both cases we construct the homogenized models and prove the convergence results. The techniques used in this work are based on a special version of the two-scale convergence method adapted to thin structures. The resulting homogenized problems are dual-porosity type models that contain terms representing memory effects.