Electronic Journal of Differential Equations,
Vol. 2008(2008), No. 14, pp. 1-18.

Title: Homogenized models for a short-time  filtration  in
       elastic porous media

Author: Anvarbek M. Meirmanov (Belgorod State Univ., Russia)

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 non-isotropic Stokes system for fluid velocity coupled
 with   two different types of acoustic equations for the solid
 component, depending on ratios between physical parameters, or
 non-isotropic Stokes system for one-velocity continuum.
 The proofs are based on Nguetseng's two-scale 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; 
           two-scale convergence; homogenization of periodic structures.