Published Paper

Inserted: 7 dec 2007
Last Updated: 10 nov 2018

Journal: Arch. Rat. Mech. Anal.
Volume: 195
Number: 1
Pages: 261-309
Year: 2010

Abstract:

We are concerned with a control problem related to the vanishing viscosity approximation to scalar conservation laws. We investigate the $\Gamma$-convergence of the control cost functional, as the viscosity coefficient tends to zero. A first order $\Gamma$-limit is established, which characterizes the measure-valued solutions to the conservation laws as the zeros of the $\Gamma$-limit. A second order $\Gamma$-limit is then investigated, providing a characterization of entropic solutions to conservation laws as the zeros of the $\Gamma$-limit.