no. 3
On the boundary conditions at the contact interface between a porous medium and a free fluid
Annali della Scuola Normale Superiore di Pisa - Classe di Scienze, Série 4, Tome 23 (1996) no. 3, pp. 403-465. 
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     title = {On the boundary conditions at the contact interface between a porous medium and a free fluid},
     journal = {Annali della Scuola Normale Superiore di Pisa - Classe di Scienze},
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Jäger, Willi; Mikelić, Andro. On the boundary conditions at the contact interface between a porous medium and a free fluid. Annali della Scuola Normale Superiore di Pisa - Classe di Scienze, Série 4, Tome 23 (1996) no. 3, pp. 403-465. http://www.numdam.org/item/ASNSP_1996_4_23_3_403_0/

[1] G. Allaire, Continuity of the Darcy's Law in the Low- Volume Fraction Limit, Ann. Scuola Norm. Sup. Pisa Cl. Sci. 18 (1991), 475-499. | Numdam | MR | Zbl

[2] G. Allaire G., Homogenization of the Stokes flow in connected porous medium, Asymptotic Anal. 3 (1989), 203-222. | MR | Zbl

[3] N. Bakhvalov N. - G. Panasenko, Homogeneisation: Averaging Processes in Periodic Media, Kluwer, Dordrecht, 1989. | MR | Zbl

[4] G.S. Beavers - D.D. Joseph, Boundary conditions at a naturally permeable wall, J. Fluid Mech. 30 (1967), 197-207.

[5] C. Conca, Étude d'unfluide traversant une paroi perforée I. Comportement limite près de la paroi, J. Math. Pures Appl. 66 (1987), 1-44. | MR | Zbl

[6] C. Conca C, Étude d'un fluide traversant une paroi perforée II. Comportement limite loin de la paroi, J. Math. Pures Appl. 66 (1987), 45-69. | MR | Zbl

[7] G. Dagan, Flow and Transport in Porous Formations, Springer, Berlin, 1989.

[8] H.I. Ene - E. Sanchez-Palencia, Equations et phénomènes de surface pour l'écoulement dans un modèle de milieu poreux., J. Mécan. 14 (1975), 73-108. | MR | Zbl

[9] G.A. Iosif'Yan G.A, An analog of Saint-Venant's principle and the uniqueness of the solutions of the first boundary value problem for Stokes system in domains with noncompact boundaries, Soviet Math. Dokl. 19 (1978), 1048-1052. | Zbl

[10] G.A. Iosif'Yan, Saint-Venant's principle for flows of a viscous incompressible fluid and its applications, Trans. Moscow Math. Soc. 43 (1983), 1-37. | Zbl

[11] W. Jäger - A. Mikeli, Homogenization of the Laplace equation in a partially perforated domain, preprint no. 157, Equipe d'Analyse Numérique, Lyon-St. Etienne, September 1993. | MR

[12] E.M. Landis - G.P. Panasenko, On a variant of a theorem of Phragmen-Lindelöf type for elliptic equations with coefficients that are periodic in all variables but one, (in Russian) Trudy Sem. Petrovski 5 (1979), 105-136. | MR | Zbl

[13] R.E. Larson - J.J.L. Higdon, Microscopic flow near the surface of two-dimensional porous media. Part I. Axial flow, J. Fluid Mech. 166 (1986), 449 - 472. | Zbl

[14] R.E. Larson - J.J.L. Higdon, Microscopic flow near the surface of two-dimensional porous media. Part II. Transverse flow, J. Fluid Mech. 178 (1986), 119-136. | Zbl

[15] Th. Levy - E. Sanchez-Palencia, On boundary conditions for fluid flow in porous media, Intemat. J. Engrg. Sci., 13 (1975), 923-940. | MR | Zbl

[16] J.L. Lions - E. Magenes, Problèmes aux limites non homogènes et applications, Vol. 1, Dunod, Paris, 1968. | MR | Zbl

[17] J.L. Lions, Some Methods in the Mathematical Analysis of Systems and Their Control, Gordon and Breach, New York, 1981. | MR | Zbl

[18] R. Lipton - M. Avellaneda, Darcy's law for slow viscous flow past a stationary array of bubbles, Proc. Royal Soc. Edinburgh, 114A (1990), 71-79. | MR | Zbl

[19] A. Mikeli, Homogenization of Nonstationary Navier-Stokes Equations in a Domain with a Grained Boundary, Annali Mat. Pura Appl. 153 (1991), 167-179. | MR | Zbl

[20] A. Mikeli - I. Aganovi, Homogenization in a Porous Medium under a Non-Homogeneous Boundary Condition, Boll. Un. Mat. Ital. 1 (1987), 171-180. | MR | Zbl

[21] O.A. Oleinik - G.A. Iosif'Yan, On the behavior at infinity of solutions of second order elliptic equations in domains with noncompact boundary, Math. USSR-Sbornik 40 (1981), 527-548. | Zbl

[22] O.A. Oleinik - A.S. Shamaev - G.A. Yosifian, Mathematical Problems in Elasticity and Homogenization, Elsevier, Amsterdam, 1992. | MR | Zbl

[23] P.G. Saffman, On the boundary condition at the interface of a porous medium, Stud. Appli. Math. 1 (1971),93-101. | Zbl

[24] E. Sanchez-Palencia, Non Homogeneous Media and Vibration Theory, Lecture Notes in Physics 127, Springer, Berlin, 1980. | MR | Zbl

[25] L. Tartar, Incompressible fluid flow in a porous medium-convergence of the homogenization process, Appendix to Lecture Notes in Physics 127, Springer, Berlin, 1980.

[26] R. Temam, Navier-Stokes Equations, North-Holland, Amsterdam, 1984. | MR | Zbl

[27] D.B. Volkov, Asymptotic expansion for solutions for Stokes' system of equations and the system of the theory of elasticity in domains of special type, U.S.S.R. Comput. Maths. Math. Phys. 23 (1983), 112-120. | MR | Zbl