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.
Gamma-entropy cost for scalar conservation laws
NOVAGA, MATTEO
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.
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