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Riemann problems with a discontinuous flux function. (English) Zbl 0789.35102
Hyperbolic problems. Theory, numerical methods and applications. Vol. I, Proc. Conf., Uppsala/Sweden 1990, 488-502 (1991).
Summary: [For the entire collection see Zbl 0758.00008.]
We study the Riemann problem for conservation laws where the flux function depends discontinuously on the space variable. We show that these Riemann problems have a unique solution provided this is picked according to a new entropy condition. It is demonstrated that this entropy condition is equivalent to the travelling wave entropy principle for an enlarged system. A numerical example is given, and an application from reservoir simulation where this phenomenon is important is presented.

MSC:
35L65 Hyperbolic conservation laws
76S05 Flows in porous media; filtration; seepage
35R05 PDEs with low regular coefficients and/or low regular data
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