On a Hamiltonian regularization of scalar conservation laws - Laboratoire Jean-Alexandre Dieudonné Accéder directement au contenu
Pré-Publication, Document De Travail Année : 2020

On a Hamiltonian regularization of scalar conservation laws

Résumé

In this paper, we study a regularization of a scalar conservation law (SCL), which is obtained by modifying its Lagrangian. This regularization is parameterized by $\ell$ and conserves formally an $H^1$-like energy. Proof of the existence of local smooth solutions are given in this paper. In addition, we prove the existence of global weak solutions satisfying a uniform (on $\ell$) one-sided Oleinik inequality for this regularization, and also for a generalized Hunter--Saxton equation. Moreover, when $\ell \to 0$ (resp. $\ell \to \infty$), we prove that the solutions of the regularized equation converge up to a subsequence to $u^0$ (resp.$ u^\infty$) a solution of the SCL (resp. a generalized Hunter--Saxton equation), at least before the appearance of singularities.
Fichier principal
Vignette du fichier
rSCL.pdf (454.37 Ko) Télécharger le fichier
Origine : Fichiers produits par l'(les) auteur(s)
Loading...

Dates et versions

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

Identifiants

  • HAL Id : hal-02512810 , version 1

Citer

Billel Guelmame. On a Hamiltonian regularization of scalar conservation laws. 2020. ⟨hal-02512810v1⟩
467 Consultations
222 Téléchargements

Partager

Gmail Facebook X LinkedIn More