Geodesic
The Muskat problem for a viscoelastic filtration
Anvarbek Meirmanov1
1Belgorod State University, Russian Federation
Interfaces and free boundaries, Tome 13 (2011) no. 4, pp. 463-484

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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.
DOI : 10.4171/ifb/268
Classification : 35-XX, 00-XX
Mots-clés : Muskat problem; free boundary problems; liquid filtration; homogenization of periodic structures; Darcy law

Anvarbek Meirmanov  1

1 Belgorod State University, Russian Federation 
Anvarbek Meirmanov. The Muskat problem for a viscoelastic filtration. Interfaces and free boundaries, Tome 13 (2011) no. 4, pp. 463-484. doi: 10.4171/ifb/268
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     title = {The {Muskat} problem for a viscoelastic filtration},
     journal = {Interfaces and free boundaries},
     pages = {463--484},
     year = {2011},
     volume = {13},
     number = {4},
     doi = {10.4171/ifb/268},
     url = {http://geodesic.mathdoc.fr/articles/10.4171/ifb/268/}
}
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