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30 September 2004 A free boundary problem describing the saturated-unsaturated flow in a porous medium
Gabriela Marinoschi
Abstr. Appl. Anal. 2004(9): 729-755 (30 September 2004). DOI: 10.1155/S1085337504311127


This paper presents a functional approach to a nonlinear model describing the complete physical process of water infiltration into an unsaturated soil, including the saturation occurrence and the advance of the wetting front. The model introduced in this paper involves a multivalued operator covering the simultaneous saturated and unsaturated flow behaviors and enhances the study of the displacement of the free boundary between these two flow regimes. The model resides in Richards' equation written in pressure form with an initial condition and boundary conditions which in this work express the inflow due to the rain on the soil surface on the one hand, and characterize a certain permeability corresponding to the underground boundary, on the other hand. Existence, uniqueness, and regularity results for the transformed model in diffusive form, that is, for the moisture of the soil, and the existence of the weak solution for the pressure form are proved in the 3D case. The main part of the paper focuses on the existence of the free boundary between the saturated and unsaturated parts of the soil, and this is proved, in the 1D case, for certain stronger assumptions on the initial data and boundary conditions.


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Gabriela Marinoschi. "A free boundary problem describing the saturated-unsaturated flow in a porous medium." Abstr. Appl. Anal. 2004 (9) 729 - 755, 30 September 2004.


Published: 30 September 2004
First available in Project Euclid: 10 October 2004

zbMATH: 1133.76350
MathSciNet: MR2102599
Digital Object Identifier: 10.1155/S1085337504311127

Primary: 35K65 , 76S05
Secondary: 47H06 , 47J35

Rights: Copyright © 2004 Hindawi

Vol.2004 • No. 9 • 30 September 2004
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