Uniqueness for scalar conservation laws with discontinuous flux via adapted entropies

By Emmanuel Audusse, Benoit Perthame. Proceedings of the Royal Society of Edinburgh. Section A Mathematics, 2005

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ON EXISTENCE AND UNIQUENESS OF ENTROPY SOLUTIONS TO THE CAUCHY PROBLEM FOR A CONSERVATION LAW WITH DISCONTINUOUS FLUX (2009, methodology): “In the same way as in paper [1] we can adapt the above proof to establish the more general comparison principle for process entropy sub- and super-solutions of (1), (2).”
Existence and Uniqueness of Entropy Solution of Scalar Conservation Laws with a Flux Function Involving Discontinuous Coefficients (2006, methodology): “, finite number of discontinuities in the solution Towers, 2000, g genuinely nonlinear Bachmann, 2004). The technical obstruction to the efficiency of the doubling of variables method is the fact that, if is an approximation of the unit, then kR x + kL y x− y vanishes only if kL = kR. But, fundament”
Existence of solutions of the hyperbolic Keller-Segel model (2006, background): “But extra terms enter into this entropy structure because of the space dependency of the flux and this leads to specific difficulties (see [3, 1, 2, 8] and the references therein).”