[Un formalisme pour la dérivation des lois de conservations]
On présente une méthode synthétique pour calculer les équations vérifiées par la dérivée par rapport à un paramètre de la solution v d'un système sous forme ∇·v=0. On montre, pour les équations de Burgers, Euler et Saint-Venant que la dérivée au sens usuel, mais interpretée au sens des distributions, contient les conditions de saut, c'est à dire les dérivées des conditions de transmission aux chocs. On retrouve ainsi les résultats de Godlewski–Raviart et al. que l'on étend aux équations d'Euler.
In this paper we present a synthetic method to differentiate with respect to a parameter partial differential equations in divergence form with shocks. We show that the usual derivatives contain the differentiated interface conditions if interpreted by the theory of distributions. We apply the method to three problems: the Burgers equation, the shallow water equations and Euler equations for fluids.
Publié le :
Claude Bardos 1 ; Olivier Pironneau 1
@article{CRMATH_2002__335_10_839_0,
author = {Claude Bardos and Olivier Pironneau},
title = {A formalism for the differentiation of conservation laws},
journal = {Comptes Rendus. Math\'ematique},
pages = {839--845},
publisher = {Elsevier},
volume = {335},
number = {10},
year = {2002},
doi = {10.1016/S1631-073X(02)02574-8},
language = {en},
}
Claude Bardos; Olivier Pironneau. A formalism for the differentiation of conservation laws. Comptes Rendus. Mathématique, Volume 335 (2002) no. 10, pp. 839-845. doi : 10.1016/S1631-073X(02)02574-8. https://comptes-rendus.academie-sciences.fr/mathematique/articles/10.1016/S1631-073X(02)02574-8/
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