Abstract
We consider the following scalar conservation law where k may be discontinuous along a finite number of possibly intersecting smooth curves in the (x, t) plane: The flux, f, is assumed to be convex in v, locally Lipschitz continuous in k and v, and grow at a superlinear rate; i.e., We will use γ(t) to denote a generic curve of discontinuity in k.These types of discontinuous k.functions occur in many different physical phenomena including traffic flow [1], continuous sedimentation [2], and shape from shading [3]. They also occur in decoupled systems of conservation laws of the form since the second equation has form (1) when the solution of the first equation has a finite number of shocks.
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Ostrov, D.N. (2001). Solutions to Scalar Conservation Laws Where the Flux is Discontinuous in Space and Time. In: Freistühler, H., Warnecke, G. (eds) Hyperbolic Problems: Theory, Numerics, Applications. ISNM International Series of Numerical Mathematics, vol 141. Birkhäuser, Basel. https://doi.org/10.1007/978-3-0348-8372-6_31
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DOI: https://doi.org/10.1007/978-3-0348-8372-6_31
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