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On conservation laws with discontinuous flux. (English) Zbl 1076.76069
Wang, Yongqi (ed.) et al., Trends in applications of mathematics to mechanics. Proceedings of the international symposium, STAMM, Seeheim, Germany, August 22–28, 2004. Aachen: Shaker (ISBN 3-8322-3600-7/pbk). Berichte aus der Mathematik, 75-84 (2005).
The authors consider two different conservation laws with discontinuous flux defined in two adjacent domains: \(u_t+f(u)_x=0\) for \(x > 0\), and \(u_t+g(u)_x = 0\), for \(x < 0\), \(t > 0\). Their applications include models of two-phase flow in porous media, traffic flows with discontinuous road surface, and clarifier-thickener models of continuous sedimentation. The main difficulty consists in the formulation of a jump criterion for the solution across the flux discontinuity. The authors introduce the entropy solution concept and present numerical schemes to treat the problem.
For the entire collection see [Zbl 1054.74003].

MSC:
76S05 Flows in porous media; filtration; seepage
76T30 Three or more component flows
74S30 Other numerical methods in solid mechanics (MSC2010)
35L65 Hyperbolic conservation laws
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