Abstract:We consider a scalar conservation law modeling the settling of particles in an ideal clarifier-thickener unit. The conservation law has a nonconvex flux which is spatially dependent on two discontinuous parameters. We suggest to use a Kru\v{z}kov-type notion of entropy solution for this conservation law and prove uniqueness ($L^1$ stability) of the entropy solution in the $BV_t$ class (functions $W(x,t)$ with $\pt W$ being a finite measure). The existence of a $BV_t$ entropy solution is established by proving convergence of a simple upwind finite difference scheme (of the Engquist-Osher type). A few numerical examples are also presented.

**Paper:**- Available as PostScript (8.7 Mbytes) or gzipped PostScript (1.5 Mbytes; uncompress using gunzip).
**Author(s):**- R. Bürger, <buerger@mathematik.uni-stuttgart.de>
- K. H. Karlsen, <kennethk@mi.uib.no>
- N. H. Risebro, <nilshr@math.uio.no>
- J. D. Towers, <jtowers@cts.com>
**Publishing information:****Comments:****Submitted by:**- <buerger@mathematik.uni-stuttgart.de> January 17 2003.

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