Asymptotic analysis of incompressible and viscous fluid flow through porous media. Brinkman's law via epi-convergence methods

 Access to full text

 Full (PDF)

1. [1] Adams ( R.A.).- Sobolev Spaces. — Academic Press, 1975. Zbl0314.46030MR450957
2. [2] Attouch ( H.).- Variational convergence for functions and operators. Applicable Mathematics series. - Pitman (London), 1984. Zbl0561.49012MR773850
3. [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. MR695419
4. [4] Brillard ( A.). — Ecoulement d'un fluide incompressible dans un milieu poreux. — Publication Avamac (Perpignan), 1985. 
5. [5] Cioranescu ( D.), and Murat ( F.).- Un terme étrange venu d'ailleurs, Collège de France Seminar.Research Notes in Maths, t. 60, 70Pitman (London), 1982. Zbl0496.35030MR652509
6. [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. Zbl0405.49001MR533166
7. [7] Ladyzhenskaya ( O.A.). — The mathematical theory of viscous incompressible flow.— Gordon and Breach (New York), 1963. Zbl0121.42701MR155093
8. [8] Levy ( T.). — Loi de Darcy ou loi de Brinkman?, C.R.A.S. série II, t. 292, 1981, p. 871-874. Zbl0485.76074MR623954
9. [9] Levy ( T.). — Fluid flow through an array of fixed particles, Int. J. Engin. Sci., t. 21 n°1, 1983, p. 11-23. Zbl0539.76092MR691100
10. [10] Marchenko, Hrouslov .— Problèmes aux limites dans des domaines aux frontières finement granulées. - in russian. Naukova Dumka (Kiev), 1974. 
11. [11] Murat ( F.).-Oral communication—1985. 
12. [12] Sanchez-Palencia ( E.).— Non-homogeneous media and vibration theory.— Lectures Notes in Physics n°127. Springer-Verlag (Berlin), 1980. Zbl0432.70002MR578345
13. [13] Tartar ( L.).- Incompressible fluid flow in a porous medium. Convergence of the homogenization process. - Appendix in the preceding reference [12]. 
14. [14] Temam ( R.). - Navier-Stokes equations.— North Holland (Amsterdam), 1977. Brinkman's law may be found in the original paper. Zbl0383.35057
15. 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. Zbl0041.54204

1. Alain Brillard, Asymptotic behaviour of a viscoplastic bingham fluid in porous media with periodic structure