Seminario di Equazioni Differenziali e Applicazioni: “Control problems related to some crowd dynamics”

Lunedì 27 Novembre 2017, ore 12:30 - Sala Riunioni VII Piano - Michel Duprez


Lunedì 27 Novembre 2017 alle ore 12:30 in Sala Riunioni VII Piano, Michel Duprez (Institut de Mathematiques de Marseille, Francia) terrà un seminario dal titolo “Control problems related to some crowd dynamics”.

We will study controllability of a Partial Differential Equation of transport type, that arises in crowd models. We are interested in controlling it with a control being a vector field, localized on a fixed control set. We will prove that, for each initial and final configuration, one can steer approximately one to another with Lipschitz controls only if the uncontrolled dynamics allows to cross the control set. The exact controllability holds only for control with less regularity. We will also study the minimal time result for such systems. We show that the minimal time to steer one initial configuration to another is related to the condition of having enough mass in the control set to feed the desired final configuration. We will finish with some numerical simulations.

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