A quantitative compactness estimate for scalar conservation laws

Camillo De Lellis; François Golse

doi:10.1002/cpa.20082

A quantitative compactness estimate for scalar conservation laws

Camillo De Lellis
, François Golse

ETH Zurich
Laboratoire de Probabilités et Modèles Aléatoires
UPMC Université de Paris VI

Résultats de recherche: Contribution à un journal › Article de révision › Revue par des pairs

Résumé

In the case of a scalar conservation law with convex flux in space dimension one, P. D. Lax proved [Comm. Pure and Appl. Math. 7 (1954)] that the semigroup defining the entropy solution is compact in L _loc ¹ for each positive time. The present note gives an estimate of the ε-entropy in L _loc ¹ of the set of entropy solutions at time t > 0 whose initial data run through a bounded set in L ¹.

langue originale	Anglais
Pages (de - à)	989-998
Nombre de pages	10
journal	Communications on Pure and Applied Mathematics
Volume	58
Numéro de publication	7
Les DOIs	https://doi.org/10.1002/cpa.20082
état	Publié - 1 juil. 2005
Modification externe	Oui

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10.1002/cpa.20082

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abstract = "In the case of a scalar conservation law with convex flux in space dimension one, P. D. Lax proved [Comm. Pure and Appl. Math. 7 (1954)] that the semigroup defining the entropy solution is compact in L loc 1 for each positive time. The present note gives an estimate of the ε-entropy in L loc 1 of the set of entropy solutions at time t > 0 whose initial data run through a bounded set in L 1.",

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AU - Golse, François

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AB - In the case of a scalar conservation law with convex flux in space dimension one, P. D. Lax proved [Comm. Pure and Appl. Math. 7 (1954)] that the semigroup defining the entropy solution is compact in L loc 1 for each positive time. The present note gives an estimate of the ε-entropy in L loc 1 of the set of entropy solutions at time t > 0 whose initial data run through a bounded set in L 1.

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DO - 10.1002/cpa.20082

M3 - Review article

AN - SCOPUS:20744455507

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JO - Communications on Pure and Applied Mathematics

JF - Communications on Pure and Applied Mathematics

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A quantitative compactness estimate for scalar conservation laws

Résumé

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