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.
Bellettini, G., Bertini, L., Mariani, M., Novaga, M. (2010). Gamma-Entropy cost for scalar conservation laws. ARCHIVE FOR RATIONAL MECHANICS AND ANALYSIS, 195(1), 261-309 [10.1007/s00205-008-0197-2].
Gamma-Entropy cost for scalar conservation laws
BELLETTINI, GIOVANNI;
2010-01-01
Abstract
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.
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https://hdl.handle.net/11365/1017501