Darcy equation for random porous media

Communications on Pure and Applied Mathematics

Volumn 49, Issue 1, 1996, Pages 1-34

  Beliaev, A Yu ^a   Kozlov, S M ^b  

^a WATER PROBLEMS INSTITUTE   (Russian Federation)

^b NONE

Author keywords

[No Author keywords available]

Indexed keywords

EID: 0030560406     PISSN: 00103640     EISSN: None     Source Type: Journal    
DOI: 10.1002/(SICI)1097-0312(199601)49:1<1::AID-CPA1>3.0.CO;2-J     Document Type: Article

References (38)

1. Allaire, G., Homogenization of the Stokes flow in a connected porous medium, Asymptotic Anal. 2, 1989, pp. 203-222.
2. Allaire, G., Continuity of the Darcy's law in the low-volume fraction limit, Ann. Scuola Norm. Sup. Pisa, Series IV 18(4), 1991, pp. 475-499.
3. Avellaneda, M., and Torquato, S., Rigorous link between fluid permeability, electrical conductivity and relaxation times for transport in porous media, Phys. Fluids A 3(11), 1991, pp. 2529-2540.
4. Banavar, J. R., and Johnson, D. Z., Characteristic pore size and transport in porous media, Phys. Rev. B 35(13), 1987, pp. 7283-7286.
5. Belyaev, A. Yu., and Kozlov, S. M., Hierarchical structures and estimates for homogenized coefficients, Russian J. Math. Phys. 1, 1992, pp. 3-15.
6. Bensoussan, A., Lions, J. L., and Papanicolaou, G., Asymptotic Analysis for Periodic Structures, North Holland, Amsterdam, 1978.
7. Bergman, D. J., Rigorous bounds for the complex dielectric constant of a two-component composite, Ann. Physics 138, 1982, pp. 78-114.
8. Bourgeat, A., and Mikelic, A., A note on the homogenization of Bingham flow through a porous medium, J. Math. Pures Appl. 72, 1993, pp. 405-414.
9. Chabi, E., and Michaille, G., Random Dirichlet problem, scalar Darcy's law, Sém. Anal. Convexe 22, Exposos 13, 1992.
10. Cioranescu, D., and Murat, F., Un terme etranger venu d'aillers, 1, pp. 98-138 in: Nonlinear Partial Differential Equations and Their Applications, College de France Seminar, Vol. 2, H. Brezis and J. L. Lions, eds., Research in Mathematics 60 Pitman, New York, 1982; Un terme etranger venu d'aillers, 2, pp. 154-178 in: Nonlinear Partial Differential Equations and Their Applications, College de France Seminar, Vol. 3, H. Brezis and J. L. Lions, eds., Research in Mathematics 60, Pitman, New York, 1982.
11. Cioranescu, D., and Murat, F., Un terme etranger venu d'aillers, 1, pp. 98-138 in: Nonlinear Partial Differential Equations and Their Applications, College de France Seminar, Vol. 2, H. Brezis and J. L. Lions, eds., Research in Mathematics 60 Pitman, New York, 1982; Un terme etranger venu d'aillers, 2, pp. 154-178 in: Nonlinear Partial Differential Equations and Their Applications, College de France Seminar, Vol. 3, H. Brezis and J. L. Lions, eds., Research in Mathematics 60, Pitman, New York, 1982.
12. Conca, C., Etude d'un fluide transversant une paroi perforée, Publ. du Lab. d'Analyse Num., Paris VI, 85008, 85018.
13. Dal Maso, G., An Introduction to Gamma Convergence, Birkhauser, Boston, 1993.
14. Donsker, M., and Varadhan, S. R. S., Asymptotics for the Wiener sausage, Comm. Pure Appl. Math. 28, 1975, pp. 525-565.
15. Ene, H. I., and Sanchez-Palencia, E., Equations et phénomënes de surfaces pour l'écoulement dans un modéle de milieux poreux, J. Méchan. 14, 1987, pp. 73-108.
16. Golden, K., and Papanicolaou, G. C., Bounds for effective parameters of heterogeneous media by analytic continuation, Comm. Math. Phys. 90, 1983, pp. 473-491.
17. Grimmett, G., Percolation, Springer-Verlag, New York, 1989.
18. Hashin, Z., and Shtrikman, S., A variational approach to the theory of effective magnetic permeability of multiphase materials, J. Appl. Mech. Tech. Phys 33, 1962, pp. 3125-3131.
19. Jikov, V. V., Kozlov, S. M., and Oleinik, O. A., Homogenization of Differential Operators and Variational Problems, Springer-Verlag, New York, 1994.
20. Kesten, H., Percolation Theory for Mathematicians, Birkhauser, Basel, Boston, 1982.
21. Kozlov, S. M., Homogenization of random operators, Mat. Sb. 109(151), 1979, pp. 188-202. (English translation in Math. USSR Sb. 37(2), 1980, pp. 167-180.)
22. Kozlov, S. M., Homogenization of random operators, Mat. Sb. 109(151), 1979, pp. 188-202. (English translation in Math. USSR Sb. 37(2), 1980, pp. 167-180.)
23. Kozlov, S. M., Averaging of difference schemes, Mat. Sb. 57(2), 1986, pp. 338-357. (English translation in Math. USSR Sb. 57(2), 1987, pp. 351-369.)
24. Kozlov, S. M., Averaging of difference schemes, Mat. Sb. 57(2), 1986, pp. 338-357. (English translation in Math. USSR Sb. 57(2), 1987, pp. 351-369.)
25. Kozlov, S. M., Geometric aspects of homogenization, Russian Math. Surveys 44(2), 1989, pp. 91-144.
26. Lebenhaft, J. R., and Kapral, R., Diffusion-controlled processes among partially absorbing stationary sinks, J. Statist. Phys. 20(1), 1979, pp. 25-56.
27. Lions, J. L., Asymptotic expansions in perforated media with a periodic structure, Rocky Mountain J. Math. 10, 1980, pp. 125-144.
28. Marchenko, V. A., and Khruslov, E. Ya., Boundary Value Problems in Domains with a Fine Grained Boundary, Naukova Dumka, Kiev, 1974.
29. Matheron, G., Elements pour une theorie des milieux poreaux, Masson, Paris, 1967.
30. Molchanov, S. A., Ruzmajkin, A. A., Sokolov, D. D., and Zel'dovich, Ya. B., Intermittency, diffusion and generation in a nonstationary random medium, Sov. Sci. Rev., Sect. C, Math. Phys. Rev. 7, 1988, pp. 1-110.
31. Murat, F., and Tartar, L., Calcul des variations et homogeneisation, Univ. Pierre et Marie Curie, Publ. Lab. d'Analyse Num., No. B84012.
32. Papanicolaou, G., Diffusion and random walks in random media, pp. 361-000 in: Mathematics and Physics of Disordered Media, B. D. Auges and B. Niham, eds., Lecture Notes in Mathematics 1035, 1983.
33. Sanchez-Palencia, E., Nonhomogeneous media and vibration theory, Lecture Notes in Phys. 127, Springer-Verlag, New York, 1980.
34. Sznitman, A. S., Brownian motion in a Poissonian potential, Probab. Theory Related Fields 95, 1993, pp. 155-174.
35. Tartar, L., Appendix in [30].
36. Taylor, M. E., Estimate on the fundamental frequency of a drum, Duke Math. J. 46(2), 1979, pp. 447-453.
37. Temam, R., Navier-Stokes Equations: Theory and Numerical Analysis, North Holland, Amsterdam, 1979.
38. Torquato, S., Random heterogeneous media: microstructure and improved bounds on effective properties, Appl. Mech. Rev. 44(2), 1991, pp. 37-74.