On a mathematical model for crowd motion

In this talk we present a new variant of the mathematical prediction-correction model for crowd motion. As the prediction step is somehow classical and performed via a transport equation, we shall focus on the correction step which relies on a minimum flow problem à la Beckmann and allows handling the congestion phenomenon. We discuss some duality results and how to solve the minimum flow problem via a primal-dual algorithm. We provide some numerical examples to illustrate our approach.