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 / G., Bellettini; BERTINI MALGARINI, Lorenzo; Mariani, Mauro; M., Novaga. - In: ARCHIVE FOR RATIONAL MECHANICS AND ANALYSIS. - ISSN 0003-9527. - 195:(2010), pp. 261-309. [10.1007/s00205-008-0197-2]
Gamma-Entropy Cost for Scalar Conservation Laws
BERTINI MALGARINI, Lorenzo;MARIANI, Mauro;
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.I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.
