Geodesic
Substantiation of the~Darcy law for a~porous medium with condition of partial adhesion
Sbornik. Mathematics, Tome 189 (1998) no. 12, pp. 1871-1888

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A study is made of a stationary Stokes's system in a periodically perforated domain with boundary conditions of mixed type, which describes the motion of a viscous incompressible fluid in a porous medium in the presence of friction between the fluid and the walls of the pores. The relation between the leading terms of the asymptotic expansions with respect to $\varepsilon$ for the fluid velocity and the pressure is obtained, where $\varepsilon$ is the parameter characterizing the fineness of the porous structure. 
@article{SM_1998_189_12_a8,
     author = {S. E. Pastukhova},
     title = {Substantiation of {the~Darcy} law for a~porous medium with condition of partial adhesion},
     journal = {Sbornik. Mathematics},
     pages = {1871--1888},
     publisher = {mathdoc},
     volume = {189},
     number = {12},
     year = {1998},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/SM_1998_189_12_a8/}
}
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S. E. Pastukhova. Substantiation of the~Darcy law for a~porous medium with condition of partial adhesion. Sbornik. Mathematics, Tome 189 (1998) no. 12, pp. 1871-1888. http://geodesic.mathdoc.fr/item/SM_1998_189_12_a8/