Gamma-entropy cost for scalar conservation laws

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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.
38 pages, 1 figure

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Analysis of PDEs, Functional Analysis, 34E99

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http://salesiana.dossiersoluciones.com/handle/123456789/168448

Consulte el texto completo en el siguiente enlace:

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

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arXiv