New entropy conditions for scalar conservation laws with discontinuous flux

Details New entropy conditions for scalar conservation laws with discontinuous flux New entropy conditions for scalar conservation laws with discontinuous flux

2010-11-18

arxiv.org/abs/1011.4236v1

Mathematics

Analysis of PDEs

21 pages, 4 figures

Scientific paper

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.

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