Czechoslovak Mathematical Journal, Vol. 71, No. 4, pp. 975-989, 2021
Application of very weak formulation on homogenization of boundary value problems
in porous media
Eduard Marušić-Paloka
Received April 22, 2020. Published online April 27, 2021.
Abstract: The goal of this paper is to present a different approach to the homogenization of the Dirichlet boundary value problem in porous medium. Unlike the standard energy method or the method of two-scale convergence, this approach is not based on the weak formulation of the problem but on the very weak formulation. To illustrate the method and its advantages we treat the stationary, incompressible Navier-Stokes system with the non-homogeneous Dirichlet boundary condition in periodic porous medium. The nonzero velocity trace on the boundary of a solid inclusion yields a non-standard addition to the source term in the Darcy law. In addition, the homogenized model is not incompressible.
Keywords: homogenization; porous medium; Navier-Stokes system; very weak formulation
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Affiliations: Eduard Marušić-Paloka, Department of Mathematics, Faculty of Science and Mathematics, University of Zagreb, Bijenička 30, 10000 Zagreb, Croatia e-mail: emarusic@math.hr
