On compactness estimates for hyperbolic systems of conservation laws
Nguyen, Khai T.; Glass, Olivier; Ancona, Fabio (2015), On compactness estimates for hyperbolic systems of conservation laws, Annales de l'Institut Henri Poincaré. Analyse non linéaire, 32, 6. http://dx.doi.org/10.1016/j.anihpc.2014.09.002
Type
Article accepté pour publication ou publiéExternal document link
http://fr.arxiv.org/pdf/1403.5070v1Date
2015Journal name
Annales de l'Institut Henri Poincaré. Analyse non linéaireVolume
32Number
6Publisher
Elsevier
Publication identifier
Metadata
Show full item recordAbstract (EN)
We study the compactness in $L^{1}_{loc}$ of the semigroup mapping $(S_t)_{t > 0}$ defining entropy weak solutions of general hyperbolic systems of conservation laws in one space dimension. We establish a lower estimate for the Kolmogorov $\varepsilon$-entropy of the image through the mapping $S_t$ of bounded sets in $L^{1}\cap L^\infty$, which is of the same order $1/\varepsilon$ as the ones established by the authors for scalar conservation laws. We also provide an upper estimate of order $1/\varepsilon$ for the Kolmogorov $\varepsilon$-entropy of such sets in the case of Temple systems with genuinely nonlinear characteristic families, that extends the same type of estimate derived by De Lellis and Golse for scalar conservation laws with convex flux. As suggested by Lax, these quantitative compactness estimates could provide a measure of the order of "resolution" of the numerical methods implemented for these equations.Subjects / Keywords
Hyperbolic systems of conservation laws; Temple systems; Compactness estimates; Kolmogorov entropyRelated items
Showing items related by title and author.
-
Ancona, Fabio; Glass, Olivier; Nguyen, Khai T. (2012) Article accepté pour publication ou publié
-
Coron, Jean-Luc; Ervedoza, Sylvain; Ghoshal, Shyam; Glass, Olivier; Perrollaz, Vincent (2017) Article accepté pour publication ou publié
-
A Remark on the Controllability of a System of Conservation Laws in the Context of Entropy Solutions Glass, Olivier (2010) Chapitre d'ouvrage
-
Glass, Olivier (2008) Article accepté pour publication ou publié
-
Coron, Jean-Michel; Glass, Olivier; Wang, Zhiqiang (2009) Article accepté pour publication ou publié