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Γ -Entropy Cost for Scalar Conservation Laws

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Date
2010
Link to item file
http://arxiv.org/abs/0712.1198v2
Dewey
Analyse
Sujet
scalar conservation laws
Journal issue
Archive for Rational Mechanics and Analysis
Volume
195
Number
1
Publication date
2010
Article pages
261-309
Publisher
Springer
DOI
http://dx.doi.org/10.1007/s00205-008-0197-2
URI
https://basepub.dauphine.fr/handle/123456789/12660
Collections
  • CEREMADE : Publications
Metadata
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Author
Bellettini, Giovanni
Bertini, Lorenzo
Mariani, Mauro
Novaga, Matteo
Type
Article accepté pour publication ou publié
Abstract (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.

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