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A rain water infiltration model with unilateral boundary condition: qualitative analysis and numerical simulations. (English) Zbl 1105.35057
Summary: We present a rigorous mathematical treatment of a model describing rain water infiltration through the vadose zone in case of runoff of the excess water. The main feature of the mathematical problem emerging from the model lies on the boundary condition on the ground surface which is in the form of a unilateral constraint. Existence and uniqueness of a weak solution is proved under general assumptions. We present also the results of a numerical study comparing the proposed model with other models which approach in a different way the rain water infiltration problem.

MSC:
35K85 Unilateral problems for linear parabolic equations and variational inequalities with linear parabolic operators
76S05 Flows in porous media; filtration; seepage
86A05 Hydrology, hydrography, oceanography
92D40 Ecology
35K60 Nonlinear initial, boundary and initial-boundary value problems for linear parabolic equations
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[1] Alt, Archive for Rational Mechanics and Analysis 64 pp 111– (1977)
[2] . In Introduction to Modeling of Transport Phenomena in Porous Media, Theory and Applications of Transport in Porous Media, (ed.), vol. 4. Kluwer: Dordrecht, 1991. · Zbl 0780.76002 · doi:10.1007/978-94-011-2632-8
[3] Dynamics of Fluids in Porous Media. American Elsevier: Amsterdam, 1972. · Zbl 1191.76001
[4] . In Modelling Groundwater Flow and Pollution, Theory and Applications of Transport in Porous Media, (ed.), vol. 1. Kluwer: Dordrecht, 1987. · doi:10.1007/978-94-009-3379-8
[5] Fasano, Journal of the Institute of Mathematics and its Applications 23 pp 503– (1979)
[6] Filo, Archive for Rational Mechanics and Analysis 146 pp 157– (1999)
[7] Gianni, Cuadernos Instituto B. Levi 18 pp 1– (1989)
[8] Otto, Advances in Mathematics and Science Applications 7 pp 537– (1997)
[9] Van Duyn, Archive for Rational Mechanics and Analysis 78 pp 173– (1982)
[10] Gianni, Bollettino Della Unione Matematica Italiana 5-B pp 875– (1991)
[11] Hanks, Water Resources Research 5 pp 1064– (1969)
[12] Feddes, Water Resources Research 6 pp 1199– (1974)
[13] Neuman, Soil Science Society of America Proceedings 39 pp 224– (1975)
[14] . Contact problems in elasticity: a study of variational inequalities and finite elements methods. SIAM Studies in Applied Mathematics, vol. 8. SIAM: Philadelphia, 1988.
[15] Huang, SIAM Journal on Mathematical Analysis 23 pp 334– (1992)
[16] Fokina, Vestnik Moskovskogo Universiteta Seriya 1 Matematika Mekhanika 30 pp 22– (1975)
[17] Partial Differential Equations of Parabolic Type. Prentice-Hall: Englewood Cliffs, NJ, 1964.
[18] , . Linear and Quasi-linear Equations of Parabolic Type. Translation of Mathematical Monographs, vol. 23. American Mathematical Society: Providence, RI, 1968.
[19] Gilding, Annali della Scuola Normale Superiore di Pisa Classe di Scienze 4 pp 393– (1977)
[20] Smith, Water Resources Research 29 pp 133– (1993)
[21] Corradini, Water Resources Research 30 pp 2777– (1994)
[22] Corradini, Journal of Hydrology 192 pp 104– (1997)
[23] Vogel, Advances in Water Resources 24 pp 133– (2001)
[24] Chen, Advances in Water Resources 22 pp 479– (1999)
[25] Peters-Lidard, Advances in Water Resources 24 pp 1069– (2001)
[26] Van Genuchten, Soil Science Society of America Journal 44 pp 892– (1980)
[27] Mualem, Water Resources Research 12 pp 513– (1976)
[28] Borsi, Nonlinear Analysis and Real World Applications 5 pp 763– (2004)
[29] Celia, Water Resources Research 26 pp 1483– (1990)
[30] , , , (eds). WR CM 90: Computational Methods in Subsurface Hydrology; Proceedings of the VIII International Conference on Computational Methods in Water Resources, Venice, Italy, 11–15 June 1990.
[31] El-Hames, Journal of Hydrology 167 pp 381– (1995)
[32] . Modelling Mathematical Methods and Scientific Computation. CRC Mathematical Modelling Series. CRC Press: Boca Raton, 1995.
[33] Aitchison, Journal of Computational and Applied Mathematics 94 pp 55– (1998)
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