Optimal Regularizing Effect for Scalar Conservation Laws

François Golse; Benoît Perthame

doi:10.4171/rmi/765

Journal articles

Optimal Regularizing Effect for Scalar Conservation Laws

François Golse ^{1, 2, *} Benoît Perthame ^{1, 3}

* Corresponding author

1 LJLL - Laboratoire Jacques-Louis Lions

2 CMLS - Centre de Mathématiques Laurent Schwartz

3 BANG - Nonlinear Analysis for Biology and Geophysical flows

LJLL - Laboratoire Jacques-Louis Lions, Inria Paris-Rocquencourt

Abstract : We investigate the regularity of bounded weak solutions of scalar conservation laws with convex flux in space dimension one, satisfying an entropy condition with entropy production term that is a signed Radon measure. The proof is based on the kinetic formulation of scalar conservation laws and on an interaction estimate in physical space.

Keywords : Scalar conservation law Compensated compactness Regularizing effect Kinetic formulation

Document type :

Journal articles

Domain :

Mathematics [math] / Analysis of PDEs [math.AP]

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https://hal-polytechnique.archives-ouvertes.fr/hal-00650350
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Submitted on : Thursday, July 26, 2012 - 10:17:29 AM
Last modification on : Friday, February 4, 2022 - 3:07:58 AM
Long-term archiving on: : Saturday, October 27, 2012 - 2:30:21 AM

Optimal Regularizing Effect for Scalar Conservation Laws

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Optimal Regularizing Effect for Scalar Conservation Laws

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