Open AccessOn the concentration of entropy for scalar conservation laws
Author(s) -
Stefano Bianchini,
Elio Marconi
Publication year - 2015
Publication title -
discrete and continuous dynamical systems - s
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.481
H-Index - 34
eISSN - 1937-1632
pISSN - 1937-1179
DOI - 10.3934/dcdss.2016.9.73
Subject(s) - conservation law , entropy (arrow of time) , scalar (mathematics) , mathematics , lagrangian , statistical physics , mathematical analysis , thermodynamics , physics , geometry
We prove that the entropy for an $L^\infty$-solution to a scalar conservation laws with continuous initial data is concentrated on a countably $1$-rectifiable set. To prove this result we introduce the notion of Lagrangian representation of the solution and give regularity estimates on the solution
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