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 . We prove also that the initial data is taken in a suitably strong sense and we give some examples which show that these results are sharp.

On the Structure of L∞ -Entropy Solutions to Scalar Conservation Laws in One-Space Dimension / Bianchini, Stefano; Marconi, Elio. - In: ARCHIVE FOR RATIONAL MECHANICS AND ANALYSIS. - ISSN 0003-9527. - 226:1(2017), pp. 441-493. [10.1007/s00205-017-1137-9]

On the Structure of L∞ -Entropy Solutions to Scalar Conservation Laws in One-Space Dimension

Bianchini, Stefano
;
Marconi, Elio
2017-01-01

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 . We prove also that the initial data is taken in a suitably strong sense and we give some examples which show that these results are sharp.
2017
226
1
441
493
http://link.springer-ny.com/link/service/journals/00205/index.htm
http://preprints.sissa.it/xmlui/handle/1963/35209
Bianchini, Stefano; Marconi, Elio
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/20.500.11767/59958
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