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

• DOI: 10.1006/jmaa.2000.6872
• Publication Date: 2002-09-18T15:51:29Z
• Authors: R. Bürger; S. Evje; K.Hvistendahl Kar...
• Keywords: Consolidation; Convection–diffusion equation

AbstractWe 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. The 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 Kružkov's method of “doubling the variables.” The application to a sedimentation–consolidation model is illustrated by two numerical examples.