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Sib. Èlektron. Mat. Izv., 2014, Volume 11, Pages 26–51 (Mi semr469)  

This article is cited in 2 scientific papers (total in 2 papers)

Differentical equations, dynamical systems and optimal control

Small perturbations of two-phase fluid in pores: effective macroscopic monophasic viscoelastic behavior

S. A. Sazhenkovab, E. V. Sazhenkovac, A. V. Zubkovab

a Novosibirsk State University, Pirogova st., 2, 630090, Novosibirsk, Russia
b Lavrentyev Institute for Hydrodynamics, Siberian Division of the Russian Academy of Sciences, pr. Acad. Lavrentyeva 15, 630090, Novosibirsk, Russia
c Novosibirsk State University of Economics and Management, Institute for Applied Informatics, Kamenskaya st., 56, 630099, Novosibirsk, Russia

Abstract: The linearized model of joint motion of an elastic porous body and a two-phase viscous compressible liquid in pores is considered. The reciprocal deformation of liquid phases is governed by Rakhmatullin’s scheme. It is assumed that the porous body has a periodic geometry and that the ratio of the pattern periodic cell and the diameter of the entire mechanical system is a small parameter in the model. The homogenization procedure, i.e. a limiting passage as the small parameter tends to zero, is fulfilled. As the result, we find that the limiting distributions of displacements of the media serve as a solution of a well-posed initial-boundary value problem for the model of linear monophasic viscoelastic material with memory of shape. Moreover, coefficients of this newly constructed model arise from microstructure, more precisely, they are uniquely defined by data in the original model. Homogenization procedure is based on the method of two-scale convergence and is mathematically rigorously justified.

Keywords: two-phase fluid in pores, homogenization of periodic structure, two-scale convergence, viscoelastic body.

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Document Type: Article
UDC: 517.958
MSC: 35B27, 35D30, 74F10
Received October 15, 2013, published January 30, 2014
Language: English

Citation: S. A. Sazhenkov, E. V. Sazhenkova, A. V. Zubkova, “Small perturbations of two-phase fluid in pores: effective macroscopic monophasic viscoelastic behavior”, Sib. Èlektron. Mat. Izv., 11 (2014), 26–51

Citation in format AMSBIB
\Bibitem{SazSazZub14}
\by S.~A.~Sazhenkov, E.~V.~Sazhenkova, A.~V.~Zubkova
\paper Small perturbations of two-phase fluid in pores: effective macroscopic monophasic viscoelastic behavior
\jour Sib. \`Elektron. Mat. Izv.
\yr 2014
\vol 11
\pages 26--51
\mathnet{http://mi.mathnet.ru/semr469}


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    This publication is cited in the following articles:
    1. V. A. Kovtunenko, A. V. Zubkova, “On generalized Poisson–Nernst–Planck equations with inhomogeneous boundary conditions: a-priori estimates and stability”, Math. Meth. Appl. Sci., 40:6 (2017), 2284–2299  crossref  mathscinet  zmath  isi  scopus
    2. V. A. Kovtunenko, A. V. Zubkova, “Solvability and Lyapunov stability of a two-component system of generalized Poisson–Nernst–Planck equations”, Recent Trends in Operator Theory and Partial Differential Equations: the Roland Duduchava Anniversary Volume, Operator Theory Advances and Applications, 258, eds. V. Mazya, D. Natroshvili, E. Shargorodsky, W. Wendland, Springer, 2017, 173–191  crossref  mathscinet  zmath  isi
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