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The Cauchy problem for an equation in the theory of infiltration. (English) Zbl 0336.76037

MSC:
76S05 Flows in porous media; filtration; seepage
35K55 Nonlinear parabolic equations
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References:
[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] Bear, J., Dynamics of Fluids in Porous Media. New York: American Elsevier Publishing Company Inc. 1972. · Zbl 1191.76001
[4] Brooks, R.H., & A.T. Corey, Properties of porous media affecting fluid flow. Journal of the Irrigation and Drainage Division ASCE 92, 61–88 (1966).
[5] Friedman, A., Partial Differential Equations of Parabolic Type. Englewood Cliffs, N.J.: Prentice-Hall Inc. 1964. · Zbl 0144.34903
[6] Gilding, B.H., Hölder continuity of solutions of parabolic equations. J. London Math. Soc. 12, (1976). · Zbl 0319.35045
[7] Irmay, S., On the hydraulic conductivity of unsaturated soils. Trans. Amer. Geophys. Union 35, 463–467 (1954).
[8] Ladyzhenskaja, O.A., V.A. Solonnikov, & N.N. Ural’ceva, Linear and Quasilinear Equations of Parabolic Type, Translations of Mathematical Monographs Volume 23. Providence, R.I.: American Mathematical Society 1968.
[9] 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 Ser. Mat. 22, 667–704 (1958).
[10] Remson, I., G.M. Hornberger, & F.J. Molz, Numerical Methods in Subsurface Hydrology with an introduction to the finite element method. New York: Wiley-Interscience 1971.
[11] Swartzendruber, D., The flow of water in unsaturated soils. Flow Through Porous Media, edited by R.J.M. Dewiest, 215–292. New York: Academic Press 1969.
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