Mathematics of Computation

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ISSN 1088-6842(e) ISSN 0025-5718(p)

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
Posted: 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 entropy solution of the problem, up to satisfaction of one of the boundary conditions.

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