Preprint 1999-022

On Strongly Degenerate Convection-Diffusion Problems Modeling Sedimentation-Consolidation Processes

Raimund Bürger, Steinar Evje, and Kenneth Hvistendahl Karlsen

Abstract: We investigate initial-boundary value problems for a quasilinear strongly degenerate convection-diffusion equation with a discontinuous diffusion coefficient. These problems come from the mathematical modeling of certain sedimentation-consolidation processes. Existence of entropy solutions belonging to $BV$ is shown by the vanishing viscosity method. The existence proof for one of the models includes a new regularity result for the integrated diffusion coefficient. New uniqueness proofs for entropy solutions are also presented. These proofs rely on a recent extension to second order equations of Kru\v{z}kov's method of ``doubling of the variables''. The application to a sedimentation-consolidation model is illustrated by two numerical examples.

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Raimund Bürger , <>
Steinar Evje , <>
Kenneth Hvistendahl Karlsen , <>
Publishing information:
Preprint (1999), University of Bergen
Submitted by:
<> August 10 16 1999.

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