Affiliations: Laboratoire de Mathématiques et de leurs Applications, CNRS-UMR 5142, Université de Pau, Av. de l'Université, 64000 Pau, France. E-mail: brahim.amaziane@univ-pau.fr | Department of Mathematics, B. Verkin Institut for Low Temperature Physics and Engineering, 47, av. Lenin, 61103, Kharkov, Ukraine. E-mail: leonid.pankratov@univ-pau.fr | ETSII, Departamento de Matemáticas, IMACI, Universidad de Castilla–la Mancha, Avda. Camilo Jose Cela, s/n, 13071 Ciudad Real, Spain. E-mail: vladyslav.prytula@uclm.es
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Abstract: In this work we consider a model problem describing one phase flow through a thin porous layer made of weakly permeable porous blocks separated by thin fissures. The flow is modeled by a linear parabolic equation considered in a bounded 2D domain with high contrast coefficients. The problem involves three small parameters: the first one characterizes the periodicity of the distribution of the blocks in the layer, the second one stands for the thickness of the layer, the third one characterizes the volume fraction of the fissure part in the layer. Using the notion of two-scale convergence, we derive the homogenized models which govern the global behavior of the flow when the small parameters tend to zero. The global models essentially depend on the relation between the small parameters.
