This paper aims at indicating research perspectives on the mathematical modeling of crowd
dynamics, pointing on the one hand to insights into the complexity features of pedestrian …

This paper introduces a new model of pedestrian flow, formulated within a measure-
theoretic framework. It consists of a macroscopic representation of the system via a family of …

In this paper, we systematically apply the mathematical structures by time-evolving
measures developed in a previous work to the macroscopic modeling of pedestrian flows …

The aim of this paper is to develop a crowd motion model designed to handle highly packed
situations. The model we propose rests on two principles: we first define a spontaneous …

Motivated by pedestrian modelling, we study evolution of measures in the Wasserstein
space. In particular, we consider the Cauchy problem for a transport equation, where the …

We consider the Volterra integro-differential equation with a time-dependent prox-regular
constraint that changes in an absolutely continuous way in time (a Volterra absolutely …

In a previous paper, we proposed a model for crowd motion, together with a numerical
algorithm, especially designed to handle highly packed situations. This model rests on two …

We propose in this paper a minimal speed-based pedestrian model for which particle
dynamics are intrinsically collision-free. The speed model is an optimal velocity function …

In this chapter we review some of the most important models at microscopic, macroscopic,
and mesoscopic scale, which, in our opinion, represent milestones in their respective fields …

This paper is devoted to the study of a new class of implicit state-dependent sweeping
processes with history-dependent operators. Based on the methods of convex analysis, we …