On the structure of $L^\infty$-entropy solutions to scalar conservation laws in one-space dimension
| dc.contributor.area | Mathematics | en_US |
| dc.contributor.author | Bianchini, Stefano | |
| dc.contributor.author | Marconi, Elio | |
| dc.date.accessioned | 2016-09-06T09:18:21Z | |
| dc.date.available | 2016-09-06T09:18:21Z | |
| dc.date.issued | 2016 | |
| dc.description.abstract | 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. | en_US |
| dc.identifier.uri | https://openscience.sissa.it/handle/1963/35209 | |
| dc.language.iso | en | en_US |
| dc.publisher | SISSA | en_US |
| dc.subject.miur | MAT/05 | en_US |
| dc.title | On the structure of $L^\infty$-entropy solutions to scalar conservation laws in one-space dimension | en_US |
| dc.type | Preprint | en_US |
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