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On the homogenization of some double-porosity models with periodic thin structures

Models describing global behaviour of incompressible flow in fractured media are discussed. A fractured medium is regarded as a porous medium consisting of two superimposed continua, a connected fracture system and a system of disjoint matrix blocks. We derive global behaviour of fractured media versus different parameters such as the fracture thickness, the size of blocks and the ratio of the block permeability and the permeability of fissures. The homogenization results are obtained by means of the convergence in domains of asymptotically vanishing measure.