Preprint 1999-022

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

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.

Paper:

Available as PostScript.

Author(s):

Raimund Bürger , <buerger@mathematik.uni-stuttgart.de>

Steinar Evje , <Steinar.Evje@rf.no>

Kenneth Hvistendahl Karlsen , <kennethk@mi.uib.no>

Publishing information:

Preprint (1999), University of Bergen

Comments:

Submitted by:

<kennethk@mi.uib.no> August 10 16 1999.