A formalism for the differentiation of conservation laws
[Un formalisme pour la dérivation des lois de conservations]
Comptes Rendus. Mathématique, Tome 335 (2002) no. 10, pp. 839-845.

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.

Accepté le :
Publié le :
DOI : 10.1016/S1631-073X(02)02574-8
Bardos, Claude 1 ; Pironneau, Olivier 1

1 Laboratoire Jacques-Louis Lions, Université Pierre et Marie Curie, 175, rue du Chevaleret, Paris 75013, France
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Bardos, Claude; Pironneau, Olivier. A formalism for the differentiation of conservation laws. Comptes Rendus. Mathématique, Tome 335 (2002) no. 10, pp. 839-845. doi : 10.1016/S1631-073X(02)02574-8. http://www.numdam.org/articles/10.1016/S1631-073X(02)02574-8/

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