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

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. 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 Kruˇzkov’s method of ‘‘doubling the variables.’’ The application to a sedimentation]consolidation model is illustrated by two numerical examples