Homogenization of a double porosity model in deformable media. (English) Zbl 1288.35038

Ainouz, Abdelhamid

Electron. J. Differ. Equ. 2013, Paper No. 90, 18 p. (2013).

Summary: 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.

MSC:

35B27	Homogenization in context of PDEs; PDEs in media with periodic structure
74Q05	Homogenization in equilibrium problems of solid mechanics
76M50	Homogenization applied to problems in fluid mechanics

Keywords:

poroelasticity equations; two-scale convergence; periodically distributed poroelastic inclusions; Biot’s system for consolidation processes; interfacial barrier formulation; memory term