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Nonstationary filtration in partially saturated porous media. (English) Zbl 0502.76101


MSC:

76S05 Flows in porous media; filtration; seepage
35A05 General existence and uniqueness theorems (PDE) (MSC2000)
35M99 Partial differential equations of mixed type and mixed-type systems of partial differential equations
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[1] Aronson, D. G., Regularity properties of flows through porous media. SIAM J. Appl. Math. 17, 461-467 (1969). · Zbl 0187.03401
[2] Aronson, D. G., Regularity properties of flows through porous media: A counterexample. SIAM J. Appl. Math. 19, 299-307 (1970). · Zbl 0255.76099
[3] Aronson, D. G., Regularity properties of flows through porous media: The interface. Arch. Rational Mech. Anal. 37, 1-10 (1970). · Zbl 0202.37901
[4] Bear, J., Dynamics of Fluids in Porous Media. New York: American Elzevier Publishing Company Inc. 1972. · Zbl 1191.76001
[5] Caffarelli, L. A., & A. Friedman, Regularity of the free boundary for the onedimensional flow of gas in a porous medium. Amer. J. Math. 101, 1193-1218 (1979). · Zbl 0439.76084
[6] Caffarelli, L. A., & A. Friedman, Continuity of a gas flow in a porous medium. Trans. Amer. Math. Soc. 252, 99-113 (1979). · Zbl 0425.35060
[7] Fasano, A., & M. Primicerio, Liquid flow in partially saturated porous media. J. Inst. Math. Appl. 23, 503-517 (1979). · Zbl 0428.76076
[8] Friedman, A., Partial differential equations of parabolic type. Prentice Hall, Englewood Cliffs, N. J. (1964). · Zbl 0144.34903
[9] Gilding, B. H., & L. A. Peletier, The Cauchy problem for an equation in the theory of infiltration. Arch. Rational Mech. Anal. 61, 127-140 (1976). · Zbl 0336.76037
[10] Kalashnikov, A. S., The occurrence of singularities in solutions of the non-steady seepage equation. USSR Computational Math, and Math. Phys. 7, 269-275 (1967).
[11] Kalashnikov, A. S., On the differential properties of generalized solutions of equations of the nonsteady-state filtration type. Vestnik Moskovskogo Universiteta Mathematika 29, 62-68 (1974). · Zbl 0272.35016
[12] Knerr, B. F., The porous media equation in one dimension. Trans. Amer. Math. Soc. 234, 381-415 (1977). · Zbl 0365.35030
[13] Ladyzhenskaja, O. A., V. A. Solonnikov & N. N. Ural’ceva, Linear and Quasilinear Equation of Parabolic Type. Translations of Mathematical Monographs Volume 23, Providence, R.I.: American Mathematical Society 1968.
[14] Oleinik, O. A., A. S. Kalashnikov & Chzhou Yui-Lin, The Cauchy problem and boundary problems for equations of the type of unsteady filtration. Izv. Akad. Nauk. SSSR Sen Mat. 22, 667-704 (1958). · Zbl 0093.10302
[15] Peletier, L. A., A necessary and sufficient condition for the existence of an interface in flows through porous media. Arch. Rational Mech. Anal. 56, 183-190 (1974). · Zbl 0294.35040
[16] Protter, M. H., & H. F. Weinberger, Maximum principles in differential equations. Prentice-Hall, Englewood Cliffs, N.J. (1967). · Zbl 0153.13602
[17] Raats, P. A. C., & W. R. Gardner, Movement of Water in the Unsaturated Zone Near a Water Table. Drainage for Agriculture, Agronomy 17, 311-405 (1974).
[18] Sabinina, E. S., On the Cauchy problem for the equation of nonstationary gas filtration in several space variables. Dokl. Akad. Nauk. SSSR 136, 1034-1037 (1961). · Zbl 0101.21101
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