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

Elio Marconi

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arXiv · 1909.07257

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

Elio Marconi

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Abstract

We consider weak solutions with finite entropy production to the scalar conservation law \begin{equation} \partial_t u+\mathrm{div}_x F(u)=0 \quad \mbox{in }(0,T)\times \mathbb{R}^d. \end{equation} Building on the kinetic formulation we prove under suitable nonlinearity assumption on $f$ 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.

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Elio Marconi. 2019-09-16. On the structure of weak solutions to scalar conservation laws with finite entropy production. https://arxiv.org/abs/1909.07257

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