Electronic Journal of Differential Equations,
Vol. 2013 (2013), No. 90, pp. 1-18.

Title: Homogenization of a double porosity model in deformable media
        
Author: Abdelhamid Ainouz (USTHB, Algiers, Algeria)

Abstract:
 The article addresses the homogenization of a family of micro-models
 for the flow of a slightly compressible fluid in a poroelastic matrix
 containing periodically distributed poroelastic inclusions, with
 low permeabilities and with imperfect contact on the interface.
 The micro-models are based on Biot's system for consolidation processes
 in each phase, with interfacial barrier formulation. Using the two-scale
 convergence technique, it is shown that the derived system is a general
 model of that proposed by Aifantis, plus an extra memory term.

Submitted November 29, 2012. Published April 05, 2013.
Math Subject Classifications: 35B27, 74Q05, 76M50.
Key Words: Poroelasticity equations; homogenization; two-scale convergence.