- journal article metadata
European Mathematical Society Publishing House
2016-09-19 17:05:03
Interfaces and Free Boundaries
Interfaces Free Bound.
IFB
1463-9963
1463-9971
Partial differential equations
Numerical analysis
Fluid mechanics
Biology and other natural sciences
10.4171/IFB
http://www.ems-ph.org/doi/10.4171/IFB
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European Mathematical Society Publishing House
Zuerich, Switzerland
© European Mathematical Society
13
2011
4
The Muskat problem for a viscoelastic filtration
Anvarbek
Meirmanov
Belgorod State University, BELGOROD, RUSSIAN FEDERATION
Muskat problem; free boundary problems; liquid filtration; homogenization of periodic structures; Darcy law
A free boundary problem describing joint filtration of two immiscible incompressible liquids is derived from homogenization theory. We start with a mathematical model on the microscopic level, which consists of the stationary Stokes system for an incompressible inhomogeneous viscous liquid, occupying a pore space, the stationary Lam´e equations for an incompressible elastic solid skeleton, coupled with suitable boundary conditions on the common boundary “solid skeleton – pore space”, and a transport equation for the unknown liquid density. Next we prove the solvability of this model and rigorously perform the homogenization procedure as the dimensionless size of pores tends to zero, while the porous body is geometrically periodic. As a result, we prove the solvability of the Muskat problem for viscoelastic filtration.
Partial differential equations
General
463
484
10.4171/IFB/268
http://www.ems-ph.org/doi/10.4171/IFB/268