Electron. J. Diff. Eqns.,
Vol. 2008(2008), No. 14, pp. 118.
Homogenized models for a shorttime filtration in
elastic porous media
Anvarbek M. Meirmanov
Abstract:
We consider a linear system of differential equations describing a
joint motion of elastic porous body and fluid occupying porous
space. The rigorous justification, under various conditions imposed
on physical parameters, is fulfilled for homogenization procedures
as the dimensionless size of the pores tends to zero, while the
porous body is geometrically periodic and a characteristic time of
processes is small enough. Such kind of models may describe, for
example, hydraulic fracturing or acoustic or seismic waves
propagation. As the results, we derive homogenized equations
involving nonisotropic Stokes system for fluid velocity coupled
with two different types of acoustic equations for the solid
component, depending on ratios between physical parameters, or
nonisotropic Stokes system for onevelocity continuum.
The proofs are based on Nguetseng's twoscale convergence method
of homogenization in periodic structures.
Submitted August 27, 2007. Published January 31, 2008.
Math Subject Classifications: 35M20, 74F10, 76S05.
Key Words: Stokes equations; Lame's equations; hydraulic fracturing;
twoscale convergence; homogenization of periodic structures.
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Anvarbek M. Meirmanov
Department of mahtematics
Belgorod State University
ul. Pobedi 85, 308015 Belgorod, Russia
email: meirmanov@bsu.edu.ru 
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