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Abstract: This paper focuses on the optimal control of weak i.e. in general nonsmooth solutions to the continuity equation with non local flow. Our drivingexamples are a supply chain model and an equation for the description ofpedestrian flows. To this aim, we prove the well posedness of a class ofequations comprising these models. In particular, we prove thedifferentiability of solutions with respect to the initial datum andcharacterize its derivative. A necessary condition for the optimality ofsuitable integral functionals then follows.



Author: Rinaldo M. Colombo, Michael Herty, Magali Mercier ICJ

Source: https://arxiv.org/







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