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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;0003-9527, 195, 1, p. 261–309. 10.1007/s00205-008-0197-2

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Type
Article accepté pour publication ou publié
Date
2010
Journal name
Archive for Rational Mechanics and Analysis;0003-9527
Volume
195
Number
1
Publisher
Elsevier
Pages
261–309
Publication identifier
Metadata
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Author(s)
Bellettini, Giovanni
Dipartimento di Matematica [Roma II] [DIPMAT]
Bertini, Lorenzo

Mariani, Mauro
CEntre de REcherches en MAthématiques de la DEcision [CEREMADE]
Novaga, Matteo
Dipartimento di Matematica [Pisa]
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 / Keywords
Radon Measure; Limit Point; Conservation Laws; Weak Solution; Entropy