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. 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. © 2000 Academic Press.