Lower compactness estimates for scalar balance laws - Inria - Institut national de recherche en sciences et technologies du numérique Accéder directement au contenu
Article Dans Une Revue Communications on Pure and Applied Mathematics Année : 2012

Lower compactness estimates for scalar balance laws

Résumé

In this paper, we study the compactness in L^{1}_{loc} of the semigroup of entropy weak solutions to strictly convex scalar conservation laws in one space dimension. The compactness of this semi-group for each time t>0 was established by P. D. Lax. Upper estimates for the Kolmogorov's epsilon-entropy of the image through the semi-group of sets bounded in L^{1} and L^\infty were given by C. De Lellis and F. Golse. Here, we provide lower estimates on this epsilon-entropy of the same order. Moreover, we extend these estimates of compactness to the case of convex balance laws.

Mots clés

Fichier principal
Vignette du fichier
CompactnessEstimates.pdf (392.95 Ko) Télécharger le fichier
Origine : Fichiers produits par l'(les) auteur(s)
Loading...

Dates et versions

hal-00606311 , version 1 (06-07-2011)
hal-00606311 , version 2 (28-10-2011)

Identifiants

  • HAL Id : hal-00606311 , version 2

Citer

Fabio Ancona, Olivier Glass, Khai Tien Nguyen. Lower compactness estimates for scalar balance laws. Communications on Pure and Applied Mathematics, 2012, 65 (9), pp.1303-1329. ⟨hal-00606311v2⟩
255 Consultations
315 Téléchargements

Partager

Gmail Facebook X LinkedIn More