On the concentration of entropy for scalar conservation laws

Stefano  Bianchini; Elio  Marconi

doi:10.3934/dcdss.2016.9.73

Article Contents

2016, Volume 9, Issue 1: 73-88. Doi: 10.3934/dcdss.2016.9.73

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On the concentration of entropy for scalar conservation laws

Stefano Bianchini^1, and
Elio Marconi^1,

1.
SISSA, via Bonomea 265, Trieste, I-34163

Received: August 31, 2014

Revised: January 31, 2015

Published: January 2016

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Abstract

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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Mathematics Subject Classification: Primary: 35L65.

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