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On the structure of $L^\infty$-entropy solutions to scalar conservation laws in one-space dimension

TitleOn the structure of $L^\infty$-entropy solutions to scalar conservation laws in one-space dimension
Publication TypePreprint
2016
AuthorsBianchini, S, Marconi, E
InstitutionSISSA

We prove that if $u$ is the entropy solution to a scalar conservation law in one space dimension, then the entropy dissipation is a measure concentrated on countably many Lipschitz curves. This result is a consequence of a detailed analysis of the structure of the
characteristics. In particular the characteristic curves are segments outside a countably
1-rectifiable set and the left and right traces of the solution exist in a $C^0$-sense up to the degeneracy due to the segments where $f''=0$. We prove also that the initial data is taken in a suitably strong sense and we give some counterexamples which show that these results are sharp.

http://urania.sissa.it/xmlui/handle/1963/35209

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