Non-local crowd dynamics

Abstract

We present a new class of macroscopic models for pedestrian flows. Each individual is assumed to move toward a fixed target, deviating from the best path according to the crowd distribution. The resulting equation is a conservation law with a non-local flux. Each equation in this class generates a Lipschitz semigroup of solutions and is stable with respect to the functions and parameters defining it. Moreover, key qualitative properties such as the boundedness of the crowd density are proved. Two specific models in this class are considered.