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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
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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

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UNIV-PARIS7 | X | UPMC | CMLS | CNRS | INRIA | INSMI | X-CMLS | X-DEP-MATH | LJLL | INRIA2 | TDS-MACS | SORBONNE-UNIVERSITE | SU-SCIENCES | UNIV-PARIS

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François Golse, Benoît Perthame. Optimal Regularizing Effect for Scalar Conservation Laws. Revista Matemática Iberoamericana, 2013, 29 (2013), pp.1477-1504. ⟨10.4171/rmi/765⟩. ⟨hal-00650350v2⟩

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