Proper entropy conditions for scalar conservation laws with discontinuous flux
Abstract: We introduce entropy admissibility conditions for scalar conservation laws with discontinuous flux which precisely describe behavior of solutions at the interface. The conditions provide well-posedness of appropriate Cauchy problem. We assume that the flux is such that the maximum principle holds, but we allow multiple flux crossings and we do not need any kind of genuine nonlinearity conditions. Proposed concept is a proper generalization to the standard Kruzhkov entropy conditions and it does not involve transformation of the equation or use of adapted entropies.