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dc.date.accessioned2013-03-12T08:19:14Z
dc.date.available2013-03-12T08:19:14Z
dc.date.issued2003en_US
dc.date.submitted2009-12-11en_US
dc.identifier.urihttp://hdl.handle.net/10852/10639
dc.description.abstractWe propose a Kruzkov-type entropy condition for nonlinear degenerate parabolic equations with discointinuous coefficients. We establish L1 stability, and thus uniqueness, for weak solutions satisfying the entropy condition, provided that the flux function satisfies a so called ```crossing condition'' and the solution satisfies a technical condition regarding the existence of traces at the jump pooints in the coefficients. In some important cases, we prove the existence of traces directly from the proposed entropy condition. We show that limits generated by the Engquist-Osher finite difference scheme and front tracking (for the hyperbolic equation) satisfy the entropy condition, and are therefore unique. By combining the uniqueness and L1 stability results of this paper with previously established existence results [27, 28], we show that the initial value problem studied herein is well-posed in some important cases. Our class of equations contains conservation laws with discontinuous coefficients as well as a certain type of singular source term.eng
dc.language.isoengen_US
dc.publisherMatematisk Institutt, Universitetet i Oslo
dc.relation.ispartofPreprint series. Pure mathematics http://urn.nb.no/URN:NBN:no-8076en_US
dc.relation.urihttp://urn.nb.no/URN:NBN:no-8076
dc.titleL¹ STABILITY FOR ENTROPY SOLUTIONS OF NONLINEAR DEGENERATE PARABOLIC CONVECTION-DIFFUSION EQUATIONS WITH DISCONTINUOUS COEFFICIENTSen_US
dc.typeResearch reporten_US
dc.date.updated2009-12-11en_US
dc.creator.authorKarlsen, Kenneth H.en_US
dc.creator.authorRisebro, Nils Henriken_US
dc.creator.authorTowers, John D.en_US
dc.subject.nsiVDP::410en_US
dc.identifier.urnURN:NBN:no-23721en_US
dc.type.documentForskningsrapporten_US
dc.identifier.duo97822en_US
dc.identifier.fulltextFulltext https://www.duo.uio.no/bitstream/handle/10852/10639/1/pm08-03.pdf


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