Gamma-entropy cost for scalar conservation laws

Details Gamma-entropy cost for scalar conservation laws Gamma-entropy cost for scalar conservation laws

2007-12-07

arxiv.org/abs/0712.1198v2

Mathematics

Analysis of PDEs

38 pages, 1 figure

Scientific paper

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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