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Flow of oil and water in a porous medium. (English) Zbl 0509.35048


MSC:

35K65 Degenerate parabolic equations
35J70 Degenerate elliptic equations
76S05 Flows in porous media; filtration; seepage
35D05 Existence of generalized solutions of PDE (MSC2000)
35B50 Maximum principles in context of PDEs
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References:

[1] Alt, H. W.; Luckhaus, S., Quasi-linear elliptic-parabolic differential equations, Math. Z., 183, 311-341 (1983) · Zbl 0497.35049
[2] Bear, J., Dynamic of Fluids in Porous Media (1972), Amer. Elsevier: Amer. Elsevier New York · Zbl 1191.76001
[3] Cannon, J. R.; Fasano, A., A nonlinear parabolic free boundary problem, Ann. Mat., 112, 119-149 (1977) · Zbl 0348.35055
[4] Collins, R. E., Flow of Fluids through Porous Materials (1961), Reinhold: Reinhold New York
[5] Ford, W. T.; Fuente, M. C.; Waid, M. C., Porous media problems, SIAM J. Math. Anal., 11, 340-347 (1980) · Zbl 0444.76068
[6] Glimm, J.; Marchesin, D.; McBryan, O., Unstable fingers in two-phase flow, Comm. Pure Appl. Math., 34, 53-76 (1981) · Zbl 0469.76078
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