dc.date.accessioned 2013-03-12T08:19:15Z dc.date.available 2013-03-12T08:19:15Z dc.date.issued 2003 en_US dc.date.submitted 2009-12-11 en_US dc.identifier.uri http://hdl.handle.net/10852/10638 dc.description.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 Kruzkov-type notion of entropy solution for this conservation law and prove iniqueness ($L_1$ 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 the Engquist-Osher type). A few numerical examples are also presented. eng dc.language.iso eng en_US dc.publisher Matematisk Institutt, Universitetet i Oslo dc.relation.ispartof Preprint series. Pure mathematics http://urn.nb.no/URN:NBN:no-8076 en_US dc.relation.uri http://urn.nb.no/URN:NBN:no-8076 dc.rights © The Author(s) (2003). This material is protected by copyright law. Without explicit authorisation, reproduction is only allowed in so far as it is permitted by law or by agreement with a collecting society. dc.title WELL-POSEDNESS IN BVt AND CONVERGENCE OF A DIFFERENCE SCHEME FOR CONTINUOUS SEDIMENTATION IN IDEAL CLARIFIER-THICKENER UNITS en_US dc.type Research report en_US dc.date.updated 2009-12-11 en_US dc.rights.holder Copyright 2003 The Author(s) dc.creator.author Bürger, Raimund en_US dc.creator.author Karlsen, Kenneth H. en_US dc.creator.author Risebro, Nils Henrik en_US dc.creator.author Towers, John D. en_US dc.subject.nsi VDP::410 en_US dc.identifier.urn URN:NBN:no-23720 en_US dc.type.document Forskningsrapport en_US dc.identifier.duo 97821 en_US dc.identifier.fulltext Fulltext https://www.duo.uio.no/bitstream/handle/10852/10638/1/pm07-03.pdf
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