Γ -Entropy Cost for Scalar Conservation Laws
Bellettini, Giovanni; Bertini, Lorenzo; Mauro, Mariani (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
TypeArticle accepté pour publication ou publié
Journal nameArchive for Rational Mechanics and Analysis
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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.
Subjects / KeywordsLarge Deviations; viscosity approximation
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