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Article Dans Une Revue Discrete and Continuous Dynamical Systems - Series A Année : 2023

On a Hamiltonian regularization of scalar conservation laws

Résumé

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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Dates et versions

hal-02512810 , version 1 (19-03-2020)
hal-02512810 , version 2 (03-04-2023)
hal-02512810 , version 3 (05-10-2023)

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  • HAL Id : hal-02512810 , version 2

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Billel Guelmame. On a Hamiltonian regularization of scalar conservation laws. Discrete and Continuous Dynamical Systems - Series A, In press. ⟨hal-02512810v2⟩
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