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Izv. RAN. Ser. Mat., 2019, Volume 83, Issue 2, Pages 142–173 (Mi izv8708)  

On homogenized equations of filtration in two domains with common boundary

A. M. Meirmanova, O. V. Galtseva, S. A. Gritsenkob

a National Research University "Belgorod State University"
b Moscow Power Engineering Institute (Technical University)

Abstract: We consider an initial-boundary value problem describing the process of filtration of a weakly viscous fluid in two distinct porous media with common boundary. We prove, at the microscopic level, the existence and uniqueness of a generalized solution of the problem on the joint motion of two incompressible elastic porous (poroelastic) bodies with distinct Lamé constants and different microstructures, and of a viscous incompressible porous fluid. Under various assumptions on the data of the problem, we derive homogenized models of filtration of an incompressible weakly viscous fluid in two distinct elastic or absolutely rigid porous media with common boundary.

Keywords: heterogeneous media, periodic structure, Lamé equations, Stokes equations, homogenization, two-scale convergence.

DOI: https://doi.org/10.4213/im8708

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English version:
Izvestiya: Mathematics, 2019, 83:2, 330–360

Bibliographic databases:

UDC: 517.958.531.33
MSC: 35Q74, 76M50, 76S05
Received: 23.08.2017
Revised: 03.08.2018

Citation: A. M. Meirmanov, O. V. Galtsev, S. A. Gritsenko, “On homogenized equations of filtration in two domains with common boundary”, Izv. RAN. Ser. Mat., 83:2 (2019), 142–173; Izv. Math., 83:2 (2019), 330–360

Citation in format AMSBIB
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  • Izvestiya Rossiiskoi Akademii Nauk. Seriya Matematicheskaya Izvestiya: Mathematics
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