Γ -Entropy Cost for Scalar Conservation Laws

Bellettini, Giovanni; Bertini, Lorenzo; Mariani, Mauro; Novaga, Matteo

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

External document link

http://arxiv.org/abs/0712.1198v2

Date

2010

Journal name

Archive for Rational Mechanics and Analysis

Volume

195

Number

Publisher

Springer

Pages

261-309

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

scalar conservation laws