Kruzkov’s estimates for scalar conservation laws revisited

Bouchut, F.; Perthame, B.

doi:10.1090/S0002-9947-98-02204-1

Kruzkov’s estimates for scalar conservation laws revisited
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by F. Bouchut and B. Perthame PDF

Trans. Amer. Math. Soc. 350 (1998), 2847-2870 Request permission

Abstract:

We give a synthetic statement of Kružkov-type estimates for multi-dimensional scalar conservation laws. We apply it to obtain various estimates for different approximation problems. In particular we recover for a model equation the rate of convergence in $h^{1/4}$ known for finite volume methods on unstructured grids.

Nous donnons un énoncé synthétique des estimations de type de Kružkov pour les lois de conservation scalaires multidimensionnelles. Nous l’appliquons pour obtenir d’estimations nombreuses pour problèmes différents d’approximation. En particulier, nous retrouvons pour une équation modèle la vitesse de convergence en $h^{1/4}$ connue pour les méthodes de volumes finis sur des maillages non structurés.

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