Authors: | Schweizer, Ben |
Title: | Regularization of outflow problems in unsaturated porous media with dry regions |
Language (ISO): | en |
Abstract: | We study a porous medium with saturated, unsaturated, and dry regions, described by Richards' equation for the saturation s and the pressure p. Due to a degenerate permeability coefficient k(x,s) and a degenerate capillary pressure function pc(x,s), the equations may be of elliptic, parabolic, or of ODE-type. We construct a parabolic regularization of the equations and find conditions that guarantee the convergence of the parabolic solutions to a solution of the degenerate system. An example shows that the convergence fails in general. Our approach provides an existence result for the outflow problem in the case of x-dependent coefficients and a method for a numerical approximation. |
URI: | http://hdl.handle.net/2003/25413 http://dx.doi.org/10.17877/DE290R-7975 |
Issue Date: | 2007-03-30 |
Provenance: | Elsevier |
URL: | http://dx.doi.org/10.1016/j.jde.2007.03.011 |
Citation: | Ben Schweizer, Regularization of outflow problems in unsaturated porous media with dry regions,. In: Journal of Differential Equations Nr. 2, Jg. 237(2007) S. 278-306. |
Appears in Collections: | Schweizer, Ben Prof. Dr. |
Files in This Item:
File | Description | Size | Format | |
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PreprintRegularizationOfOutflow.pdf | 275.71 kB | Adobe PDF | View/Open |
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