References
- Beavers , GS and Joseph , DD . 1967 . Boundary conditions at a naturally permeable wall . J. Fluid Mech. , 30 : 197 – 207 .
- Brillard , A . 1986 . Asymptotic analysis of incompressible fluid flow through porous media. Brinkman's law via epi-convergence methods . Ann. Fac. Sci. Toulouse , 8 ( 2 ) : 225 – 252 .
- Cieszko , M and Kubik , J . 1999 . Derivation of matching conditions at the contact surface between fluid-saturated porous solid and bulk fluid . Transp. Porous Media , 34 : 319 – 336 .
- Jäger , W and Mikelic , A . 1996 . On the boundary conditions at the contact interface between a porous medium and a free fluid . Ann. Scuola Normale Sup. Pisa Cl. Sci. (4) , 23 : 403 – 465 .
- Jäger , W and Mikelic , A . 2000 . On the interface boundary condition of Beavers, Joseph and Saffman . SIAM J. Applied Mathematics , 60 : 1111 – 1127 .
- Jäger , W and Mikelic , A . 2009 . Modeling interface laws for transport phenomena between an unconfined fluid and a porous medium using homogenization . Transp. Porous Media , 78 ( 3 ) : 489 – 508 .
- Saffman , PG . 1971 . On the boundary condition at the interface of a porous medium . Stud. Appl. Math. , 1 : 93 – 101 .
- Ripperger , S and Altmann , J . 2002 . Crossflow microfiltration – State of the art . Sep. Purif. Technol. , 26 : 19 – 31 .
- Temam , R . 1984 . Navier–Stokes Equations. Theory and Numerical Analysis, Studies in Maths and its Applications , Vol. 2 , Amsterdam : North-Holland .
- Attouch , H . 1984 . “ Variational Convergence for Functions and Operators ” . In Applied Mathematics Series , London : Pitman .
- Dal Maso , G . 1993 . “ An Introduction to Γ-Convergence ” . In Progress in Nonlinear Differential Equations and Applications , Vol. 8 , Basel : Birkhäuser .
- Nguetseng , G . 1989 . A general convergence result for a functional related to the theory of homogenization . SIAM J. Math. Anal. , 20 ( 3 ) : 608 – 623 .
- El Jarroudi , M . 2010 . Homogenization of an incompressible viscous flow in a porous medium with double porosity . Z. Angew. Math. Phys. , 61 ( 6 ) : 1053 – 1083 .
- Bogovskii , ME . 1980 . Solutions of some problems of vector analysis, associated with the operators div and grad . Trudy Sem. S.L. Soboleva , 1 : 5 – 41 . (in Russian)
- Marchenko , VA and Hruslov , EJa . 1974 . Boundary value problems in the regions with a fine-grain boundary , Kiev : Naukova Dumka . (in Russian)
- Allaire , G . 1989 . Homogenization of the Stokes flow in connected porous medium . Asympt. Anal. , 2 ( 3 ) : 203 – 222 .
- Sanchez-Palencia , E . 1980 . Non-homogeneous Media and Vibration Theory, Lecture Notes in Physics , Vol. 127 , Berlin : Springer-Verlag .
- Landis , EM and Panasenko , GP . 1979 . On a variant of theorem of Phragmen-Lindelöf type for elliptic equations with coefficients that are periodic in all variables but one . Trudy Sem. Petrovski , 5 : 105 – 136 . (in Russian)
- Oleinik , OA , Shamaev , AS and Yosifian , GA . 1992 . Mathematical Problems in Elasticity and Homogenization, Studies in Maths and its Applications , Vol. 26 , Amsterdam : North-Holland .