Abstract
We provide an informal presentation of the work mainly contained in Bianchini and Marconi, On the structure of \(L^{\infty }\) entropy solutions to scalar conservation laws in one-space dimension, [3]. We consider the entropy solution u of a scalar conservation law in one-space dimension. In particular, we prove that the entropy dissipation is a measure concentrated on countably many Lipschitz curves. This follows from a detailed analysis of the structure of the characteristics. We will introduce a few notions of Lagrangian representations and we prove that characteristics are segments outside a countably 1-rectifiable set.
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Bianchini, S., Marconi, E. (2018). A Lagrangian Approach to Scalar Conservation Laws. In: Klingenberg, C., Westdickenberg, M. (eds) Theory, Numerics and Applications of Hyperbolic Problems I. HYP 2016. Springer Proceedings in Mathematics & Statistics, vol 236. Springer, Cham. https://doi.org/10.1007/978-3-319-91545-6_14
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DOI: https://doi.org/10.1007/978-3-319-91545-6_14
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