Calculus of Variations and Geometric Measure Theory

S. Bianchini - E. Marconi

On the concentration of entropy for scalar conservation laws

created by marconi on 13 Aug 2016


Published Paper

Inserted: 13 aug 2016
Last Updated: 13 aug 2016

Journal: Discrete and Continuous Dynamical Systems. Series S
Volume: 9
Number: 1
Pages: 73--88
Year: 2016
Doi: 10.3934/dcdss.2016.9.73


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.

Keywords: shocks, concentration, Conservation laws, entropy solutions, Lagrangian representation