2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/168448We 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 figureAnalysis of PDEsFunctional Analysis34E99text