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The homogenization of compressible flows in a random porous domain. (English) Zbl 0898.76092
Cioranescu, Doina (ed.) et al., Homogenization and applications to material sciences. Proceedings of the international conference, Nice, France, June 6–10, 1995. Tokyo: Gakkotosho. GAKUTO Int. Ser., Math. Sci. Appl. 9, 31-43 (1995).
Summary: This paper deals with the homogenization of unsteady Stokes equations in random porous domains. In this asymptotic problem Darcy law and parabolic homogenized equation are established for the leading term of the solution. The random structure is supposed statistically homogeneous with respect to the group of translations in \(\mathbb{R}^n\). The main geometric condition for the porous domain is its connectedness. The complement to this domain could be either connected or disconnected. Smoothness or regularity of boundaries are not assumed.
For the entire collection see [Zbl 0873.00028].

76S05 Flows in porous media; filtration; seepage
76N10 Existence, uniqueness, and regularity theory for compressible fluids and gas dynamics
35B27 Homogenization in context of PDEs; PDEs in media with periodic structure