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New entropy conditions for scalar conservation laws with discontinuous flux

We propose new Kruzhkov type entropy conditions for one dimensional scalar conservation law with a discontinuous flux. We prove existence and uniqueness of the entropy admissible weak solution to the corresponding Cauchy problem merely under assumptions on the flux which provide the maximum principle. In particular, we allow multiple flux crossings and we do not need any kind of genuine nonlinearity conditions.

preprint2010arXivOpen access
Darko Mitrovic
math.AP
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Darko Mitrovic

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