Control of crowds: analysis and numerics

Supervisor
Francesco Rossi - Aix-Marseille Université
Date and time
Thursday, May 19, 2016 at 11:00 AM - Rinfresco 10.45, inizio seminario 11.00
Place
Ca' Vignal - Piramide, Floor 0, Hall Verde
Programme Director
External reference
Antonio Marigonda
Publication date
April 25, 2016
Department
Computer Science  

Summary

In this talk, we first present transport equations with non-local velocities, that are used in several models of pedestrian crowds, road traffic and opinion dynamics. We describe a complete framework for existence and uniqueness of solutions in Wasserstein spaces [1,2]. We then define some numerical schemes to compute solutions, and prove their convergence [1]. Finally, we describe our recent results of control of transport equations, focusing in particular on cooperative crowds, such as the Cucker-Smale model [3].

[1] B. Piccoli, F. Rossi, Transport equation with nonlocal velocity in Wasserstein spaces: convergence of numerical schemes, Acta Applicandae Mathematicae, 124, pp. 73-105, 2013.
[2] P. Goatin, F. Rossi, A traffic flow model with non-smooth metric interaction: well-posedness and micro-macro limit, Comm. Math Sciences, to appear, arXiv:1510.04461.
[3] B. Piccoli, F. Rossi, E. Trélat, Control to flocking of the kinetic Cucker-Smale model, SIAM J. Mathematical Analysis 47, no. 6, pp. 4685-4719, 2015.

 





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