On nonstationary flow through porous media. (English) Zbl 0552.76075

The authors deal with saturated-unsaturated flow of an incompressible fluid through a porous medium in the case of time dependent water levels [see also A. Torelli, Boll. Unione Mat. Ital., IV. Ser. 11, 559-570 (1975; Zbl 0331.76058); G. Gilardi, Commun. Partial Differ. Equations 4, 1099-1122 (1979; Zbl 0426.35096); the third author, Ann. Mat. Pura Appl., IV. Ser. 124, 293-320 (1980; Zbl 0445.76078)]. The existence of the corresponding weak solution is obtained. Strong convergence of the saturation in one space dimension is proved.
Reviewer: Yu.E.Hohlov


76S05 Flows in porous media; filtration; seepage
35R35 Free boundary problems for PDEs
Full Text: DOI


[1] Alt, H. W., Strömungen durch inhomogene poröse Medien mit freiem Rand, J. Reine Angew. Matt., 305, 89-115 (1979) · Zbl 0392.76091
[2] Alt, H. W., The dam problem, Free boundary problems: theory and applications, I 52-68 (1983), Boston-London-Melbourne: Pitman, Boston-London-Melbourne
[3] Alt, H. W.; Luckhaus, S., Quasilinear elliptic-parabolic differential equations, Math. Z., 183, 311-341 (1983) · Zbl 0497.35049
[4] Baiocchi, C., Su un problema di frontiera libera connesso a questioni di idraulica, Ann. Mat. Pura e Appl., 92, 107-127 (1972) · Zbl 0258.76069
[5] Bear, J., Dynamic of fluids in porous media (1972), New York: American Elsevier, New York · Zbl 1191.76001
[6] Benilan, P., Equations d’évolutions dans un espace de Banach quelconque et applications, Thèse (1972), Orsay: Univ. Paris XI, Orsay
[7] Gilardi, G., A new approach to evolution free boundary problems, Comm. on Part. Diff. Eq., 4, 1099-1122 (1979) · Zbl 0426.35096
[8] Hornung, U., A parabolic-elliptic variational inequality, Manuscripta Mathematica, 39, 155-172 (1982) · Zbl 0502.35055
[9] Lions, J. L., Quelques méthodes de résolution des problèmes aux limites non linéaires (1969), Paris: Dunod, Gauthier-Villars, Paris · Zbl 0189.40603
[10] Tartar, L.; Knops, R. J., Compensated compactness and applications to partial differential equations, Nonlinear Analysis and Mechanics, Heriot-Watt Symposium, vol. IV, 136-212 (1979), London: Pitman, London
[11] Torelli, A., Su un problema a frontiera libera di evoluzione, Boll. Un. Mat. Ital., (4), 11, 559-570 (1975) · Zbl 0331.76058
[12] Visintin, A., Existence results for some free boundary filtration problems, Ann. Mat. Pura e Appl., 124, 293-320 (1980) · Zbl 0445.76078
[13] A.Visintin,Strong convergence results related to strict convexity, submitted to Comm. on Part. Diff. Eq. · Zbl 0545.49019
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.