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Γ -Entropy Cost for Scalar Conservation Laws

Bellettini, Giovanni; Bertini, Lorenzo; Mariani, Mauro; Novaga, Matteo (2010), Γ -Entropy Cost for Scalar Conservation Laws, Archive for Rational Mechanics and Analysis, 195, 1, p. 261-309. http://dx.doi.org/10.1007/s00205-008-0197-2

Type
Article accepté pour publication ou publié
Lien vers un document non conservé dans cette base
http://arxiv.org/abs/0712.1198v2
Date
2010
Nom de la revue
Archive for Rational Mechanics and Analysis
Volume
195
Numéro
1
Éditeur
Springer
Pages
261-309
Identifiant publication
Métadonnées
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Auteur(s)
Bellettini, Giovanni
Bertini, Lorenzo
Mariani, Mauro
Novaga, Matteo
Résumé (EN)
We are concerned with a control problem related to the vanishing viscosity approximation to scalar conservation laws. We investigate the Γ -convergence of the control cost functional, as the viscosity coefficient tends to zero. A first-order Γ -limit is established, which characterizes the measure-valued solutions to the conservation laws as the zeros of the Γ -limit. A second-order Γ -limit is then investigated, providing a characterization of entropic solutions to conservation laws as the zeros of the Γ -limit.
Mots-clés
scalar conservation laws