Calculus of Variations and Geometric Measure Theory
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G. Bellettini - L. Bertini - M. Mariani - M. Novaga

$\Gamma$-entropy cost for scalar conservation laws

created by novaga on 07 Dec 2007
modified on 10 Nov 2018


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


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.

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