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.