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Izvestiya: Mathematics, 2019, Volume 83, Issue 2, Pages 330–360
DOI: https://doi.org/10.1070/IM8708 (Mi im8708) 		 
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)
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DOI: https://doi.org/10.1070/IM8708
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.
Received: 23.08.2017
Revised: 03.08.2018
Russian version:
Izvestiya Rossiiskoi Akademii Nauk. Seriya Matematicheskaya, 2019, Volume 83, Issue 2, Pages 142–173
DOI: https://doi.org/10.4213/im8708
Bibliographic databases:
Document Type: Article
UDC: 517.958.531.33
MSC: 35Q74, 76M50, 76S05
Language: English
Original paper language: Russian
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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    		Известия Российской академии наук. Серия математическая Izvestiya: Mathematics
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    References:57
    First page:38
     
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