Abstract
Unsteady saturated/unsaturated waterflow in porous media can be described by a degenerate nonlinear Fokker-Planck differential equation. An initial/boundary value problem is formulated as an initial value problem for an evolution equation in Hilbert space. Using the theory of maximal monotone operators, existence and uniqueness of solutions can be proved. The same holds for the discretized problem that is obtained from the continuous problem by the longitudinal line method.
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Literatur
Brezis, H.: Monotonicity Methods in Hilbert Spaces and Some Applications to Nonlinear Partial Differential Equations. In Zarantonello, E.H.(Ed.): Contributions to Nonlinear Functional Analysis. New York-London, Academic Press 1971, 101–156.
Brezis, H.: Operateurs Maximaux Monotones et semi-groupes de contractions dans les espaces de Hilbert. Amsterdam-London, North-Holland 1973.
Byrne, G.D., Hindmarsh, A.C.: A Polyalgorithm for the Numerical Solution of Ordinary Differential Equations. ACM Trans. Math. Software 1 (1975), 71–96.
Carroll, R.W., Showalter, R.E.: Singular and Degenerate Cauchy Problems. New York-San Francisco-London, Academic Press 1976.
Curtiss, CF., Hirschfelder, J.O.: Integration of Stiff Equations. Proc. Nat. Acad. Science, U.S., 38 (1952), 235–243.
Hornung, U.: A Numerical Method for the Simulation of Unsteady Ground-Water Flow in Both Saturated and Unsaturated Soils. Soil Science 124 (1977).
Neuman, S.P.: Galerkin Approach to Saturated-Unsaturated Flow in Porous Media. In Gallagher, R.H., Oden, J.T., Taylor, C., Zienkiewicz, O.C. (Ed.): Finite Elements in Fluids I, London-New York-Sydney-Toronto, Academic Press 1975, 201–217.
Philip, J.R.: The Theory of Infiltration: 1. The Infiltration Equation and Its Solution. Soil Science 83 (1957), 345–357.
Torelli, A.: Un problème à frontière libre d’évolution en hydraulique. C.R. Acad.Sc.Paris 280 (1975) Ser. A, 353–356.
Torelli, A.: Su un problema non lineare con una condizione di evoluzione sulla frontiera. Ann. Mat. Pura Appl. Ser. 4, 112 (1977), 91–106.
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Hornung, U. (1978). Numerische Simulation von Gesättigt-Ungesättigten Wasserflüssen in Porösen Medien. In: Albrecht, J., Collatz, L., Hämmerlin, G. (eds) Numerische Behandlung von Differentialgleichungen mit besonderer Berücksichtigung freier Randwertaufgaben. International Series of Numerical Mathematics / Internationale Schriftenreihe zur Numerischen Mathematik / Série Internationale D’Analyse Numérique, vol 39. Birkhäuser, Basel. https://doi.org/10.1007/978-3-0348-5566-2_12
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DOI: https://doi.org/10.1007/978-3-0348-5566-2_12
Publisher Name: Birkhäuser, Basel
Print ISBN: 978-3-7643-0986-2
Online ISBN: 978-3-0348-5566-2
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