an:02077950
Zbl 1053.76047
B??rger, R.; Karlsen, K. H.; Risebro, N. H.; Towers, J. D.
Well-posedness in \(BV_t\) and convergence of a difference scheme for continuous sedimentation in ideal clarifier-thickener units
EN
Numer. Math. 97, No. 1, 25-65 (2004).
00104150
2004
j
76M20 76T20 65M12 65M06 35L65 35R05
Kru??kov entropy solution; scalar conservation law; uniqueness
Summary: 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 Kruzhkov-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 \(\partial_tW\) 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 Engquist-Osher type). A few numerical examples are also presented.