2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/219997This paper focuses on the optimal control of weak (i.e. in general non smooth) solutions to the continuity equation with non local flow. Our driving examples are a supply chain model and an equation for the description of pedestrian flows. To this aim, we prove the well posedness of a class of equations comprising these models. In particular, we prove the differentiability of solutions with respect to the initial datum and characterize its derivative. A necessary condition for the optimality of suitable integral functionals then follows.Analysis of PDEsOptimization and Control35L65, 49K20, 93C20text