On Strongly Degenerate Convection–Diffusion Problems Modeling Sedimentation–Consolidation Processes
✍ Scribed by R. Bürger; S. Evje; K.Hvistendahl Karlsen
- Publisher
- Elsevier Science
- Year
- 2000
- Tongue
- English
- Weight
- 294 KB
- Volume
- 247
- Category
- Article
- ISSN
- 0022-247X
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✦ Synopsis
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 Kruzkov's method of ''doubling the variables.''
The application to a sedimentation᎐consolidation model is illustrated by two numerical examples.