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arXiv · 2403.02218

On a Hamiltonian regularization of scalar conservation laws

Billel Guelmame
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Abstract

In this paper, we propose a Hamiltonian regularization of scalar conservation laws, which is parametrized by $\ell > 0$ and conserves an $H^1$ energy. We prove the existence of global weak solutions for this regularization. Furthermore, we demonstrate that as $\ell$ approaches zero, the unique entropy solution of the original scalar conservation law is recovered, providing justification for the regularization. This regularization belongs to a family of non-diffusive, non-dispersive regularizations that were initially developed for the shallow-water system and extended later to the Euler system. This paper represents a validation of this family of regularizations in the scalar case.

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Billel Guelmame. 2024-03-04. On a Hamiltonian regularization of scalar conservation laws. https://doi.org/10.3934/dcds.2023118

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