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.
mailto:conservation@math.ntnu.no Last modified: Wed Aug 11 09:47:47 1999