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A semi-implicit monotone difference scheme for an initial-boundary value problem of a strongly degenerate parabolic equation modeling sedimentation-consolidation processes

Authors: Raimund Bürger, Aníbal Coronel and Mauricio Sepúlveda
Journal: Math. Comp. 75 (2006), 91-112
MSC (2000): Primary 35L65, 35R05, 65M06, 76T20
Published electronically: October 21, 2005
MathSciNet review: 2176391
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Abstract: We prove the convergence of a semi-implicit monotone finite difference scheme approximating an initial-boundary value problem for a spatially one-dimensional quasilinear strongly degenerate parabolic equation, which is supplied with two different inhomogeneous flux-type boundary conditions. This problem arises in the modeling of the sedimentation-consolidation process. We formulate the definition of entropy solution of the model in the sense of Kru $ \check{\mbox{z}}$kov and prove convergence of the scheme to the unique $ BV$ entropy solution of the problem, up to satisfaction of one of the boundary conditions.

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Additional Information

Raimund Bürger
Affiliation: Departamento de Ingeniería Matemática, Universidad de Concepción, Casilla 160-C, Concepción, Chile

Aníbal Coronel
Affiliation: Departamento de Ciencias Básicas, Facultad de Ciencias, Universidad del Bío-Bío, Casilla 447, Campus Fernando May, Chillán, Chile

Mauricio Sepúlveda
Affiliation: Departamento de Ingeniería Matemática, Universidad de Concepción, Casilla 160-C, Concepción, Chile

Keywords: Degenerate parabolic equation, monotone scheme, upwind difference scheme, boundary conditions, entropy solution
Received by editor(s): May 18, 2004
Received by editor(s) in revised form: January 18, 2005
Published electronically: October 21, 2005
Additional Notes: We acknowledge support by FONDECYT projects 1030718 and 1050728, Fondap in Applied Mathematics, the German Acadamic Exchange Service (DAAD) and CONICYT (Chile) through project Alechile/DAAD/CONICYT 2003154, and the Sonderforschungsbereich 404 at the University of Stuttgart.
Article copyright: © Copyright 2005 American Mathematical Society
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