Asymptotic analysis of incompressible and viscous fluid flow through porous media. Brinkman's law via epi-convergence methods
Annales de la Faculté des sciences de Toulouse : Mathématiques, Série 5, Tome 8 (1986-1987) no. 2, pp. 225-252. 
@article{AFST_1986-1987_5_8_2_225_0,
     author = {Brillard, Alain},
     title = {Asymptotic analysis of incompressible and viscous fluid flow through porous media. {Brinkman's} law via epi-convergence methods},
     journal = {Annales de la Facult\'e des sciences de Toulouse : Math\'ematiques},
     pages = {225--252},
     publisher = {Universit\'e Paul Sabatier},
     address = {Toulouse},
     volume = {Ser. 5, 8},
     number = {2},
     year = {1986-1987},
     mrnumber = {928845},
     zbl = {0628.76093},
     language = {en},
     url = {http://www.numdam.org/item/AFST_1986-1987_5_8_2_225_0/}
}
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Brillard, Alain. Asymptotic analysis of incompressible and viscous fluid flow through porous media. Brinkman's law via epi-convergence methods. Annales de la Faculté des sciences de Toulouse : Mathématiques, Série 5, Tome 8 (1986-1987) no. 2, pp. 225-252. http://www.numdam.org/item/AFST_1986-1987_5_8_2_225_0/

[1] Adams (R.A.).- Sobolev Spaces. - Academic Press, 1975. | MR | Zbl

[2] Attouch (H.).- Variational convergence for functions and operators. Applicable Mathematics series. - Pitman (London), 1984. | MR | Zbl

[3] Attouch (H.), and Picard (C.). - Variational inequalities with varying obstacles; the general form of the limit problem, J.Functional Analysis, t. 50 (3), 1983, p. 329-386. | MR

[4] Brillard (A.). - Ecoulement d'un fluide incompressible dans un milieu poreux. - Publication Avamac (Perpignan), 1985.

[5] Cioranescu (D.), and Murat (F.).- Un terme étrange venu d'ailleurs, Collège de France Seminar. Research Notes in Maths, t. 60, 70 Pitman (London), 1982. | MR | Zbl

[6] De Giorgi (E.).- Convergence problems for functionals and operators. Proc. Int. Congress on "Recent Methods in Nonlinear Analysis" Rome 1978 De Giorgi, Magenes, Mosco Eds. Pitagora Editrice (Bologna) 1979. | MR | Zbl

[7] Ladyzhenskaya (O.A.). - The mathematical theory of viscous incompressible flow.- Gordon and Breach (New York), 1963. | MR | Zbl

[8] Levy (T.). - Loi de Darcy ou loi de Brinkman?, C.R.A.S. série II, t. 292, 1981, p. 871-874. | MR | Zbl

[9] Levy (T.). - Fluid flow through an array of fixed particles, Int. J. Engin. Sci., t. 21 n°1, 1983, p. 11-23. | MR | Zbl

[10] Marchenko, Hrouslov .- Problèmes aux limites dans des domaines aux frontières finement granulées. - in russian. Naukova Dumka (Kiev), 1974.

[11] Murat (F.).-Oral communication-1985.

[12] Sanchez-Palencia (E.).- Non-homogeneous media and vibration theory.- Lectures Notes in Physics n°127. Springer-Verlag (Berlin), 1980. | MR | Zbl

[13] Tartar (L.).- Incompressible fluid flow in a porous medium. Convergence of the homogenization process. - Appendix in the preceding reference [12].

[14] Temam (R.). - Navier-Stokes equations.- North Holland (Amsterdam), 1977. Brinkman's law may be found in the original paper. | Zbl

Brinkman (H.C.).-A calculation of the viscous force exerted by a flowing fluid on a dense swarm of particles, Appli. Sci. Res., t. A1, 1947, p. 27-34. | Zbl