Nonsteady flow of water and oil through inhomogeneous porous media
Annali della Scuola Normale Superiore di Pisa - Classe di Scienze, Série 4, Volume 12 (1985) no. 3, p. 335-392
@article{ASNSP_1985_4_12_3_335_0,
     author = {Alt, Hans Wilhelm and Di Benedetto, E.},
     title = {Nonsteady flow of water and oil through inhomogeneous porous media},
     journal = {Annali della Scuola Normale Superiore di Pisa - Classe di Scienze},
     publisher = {Scuola normale superiore},
     volume = {Ser. 4, 12},
     number = {3},
     year = {1985},
     pages = {335-392},
     zbl = {0608.76082},
     mrnumber = {837254},
     language = {en},
     url = {http://www.numdam.org/item/ASNSP_1985_4_12_3_335_0}
}
Alt, H. W.; Di Benedetto, E. Nonsteady flow of water and oil through inhomogeneous porous media. Annali della Scuola Normale Superiore di Pisa - Classe di Scienze, Série 4, Volume 12 (1985) no. 3, pp. 335-392. http://www.numdam.org/item/ASNSP_1985_4_12_3_335_0/

[1] H.W. Alt - S. Luckhaus, Quasilinear elliptic -parabolic differential equations, Preprint 136, SFB 123, Heidelberg, and Math. Z., 183 (1983), pp. 311-341. | MR 706391 | Zbl 0497.35049

[2] J. Bear, Dynamics of fluids in porous media, American Elsevier, New York, 1972. | Zbl 1191.76001

[3] J. Bear, Hydraulics of Groundwater, Mc-Graw Hill, New York, 1979.

[4] R.E. Collins, Flow of fluids through porous materials, Reinhold, New York, 1961.

[5] E. Dibenedetto, Continuity of weak solutions to certain singular parabolic equations, Ann. Mat. Pura Appl., (IV), 130 (1982), pp. 131-177. | MR 663969 | Zbl 0503.35018

[6] J. Douglasjr., Finite difference methods for two-phase incompressible flow in porous media, Siam J. Numer. Anal., 20 (1983), pp. 681-696. | MR 708451 | Zbl 0519.76107

[7] J. Douglasjr. - B.L. Darlow - M.F. Wheeler - R.P. Kendall, Self-adaptive finite element and finite difference methods for two-phase immiscible flow, to appear. | Zbl 0535.76121

[8] J. Glimm - D. Marchesin - O. McBRYAN, Unstable fingers in two phase flow, Comm. Pure Appl. Math., 34 (1981), pp. 53-76. | MR 600572 | Zbl 0469.76078

[9] D. Kröner - S. Luckhaus, Flow of oil and water in a porous medium, J. Differential Equations, 55 (1984), pp. 276-288. | MR 764127 | Zbl 0509.35048

[10] S.N. Kruzkov - S.M. Sukorjanski, Boundary value problems for systems of equations of two phase porous flow type: statement of the problems, questions of solvability, justification of approximate methods, Mat. Sb., 33 (1977), pp. 62-80. | Zbl 0398.35039

[11] O.A. Ladyzenskaja - N.N. Urel'Tzeva, Linear and quasi-linear equations of elliptic type, Academic Press, New York (1968).

[12] O.A. Ladyzenskaja - V.A. Solonnikov - N.N. Ural'Tzeva, Linear and quasi-linear equations of parabolic type, Amer. Math. Soc. Transl. Math. Mono, vol. 23 (Providence, R.I., 1968). | Zbl 0174.15403

[13] M.C. Leverett, Capillary behavior in porous solids, Trans. Amer. Inst. Mining and Metallurgical Engrs., 142 (1941), pp. 152-169.

[14] A.E. Scheidegger, The Physics of flow through porous media, 3rd ed., Univ. of Toronto Press, Toronto, Ontario, 1974. | Zbl 0095.22402

[15] A. Spivak - H.S. Price - A. Settari, Solution of the equations for multidimensional, two-phase, immiscible flow by variational methods, Soc. Pet. Eng. J., Feb. 1977, pp. 27-41.