On the structure of weak solutions to scalar conservation laws with finite entropy production

created by marconi on 16 Sep 2019
modified on 13 Sep 2021

[BibTeX]

Accepted Paper

Inserted: 16 sep 2019
Last Updated: 13 sep 2021

Journal: Calc. Var. PDEs
Year: 2019

Abstract:

We consider weak solutions $u$ with finite entropy production to scalar conservation laws in $d$-space dimensions. Building on the kinetic formulation we prove under suitable nonlinearity assumption on the flux $f$ that the set of non Lebesgue points of $u$ has Hausdorff dimension at most $d$. A notion of Lagrangian representation for this class of solutions is introduced and this allows for a new interpretation of the entropy dissipation measure.