Nonlocal Crowd Dynamics Models for several Populations

Rinaldo M. Colombo (1) , Magali Lécureux-Mercier (2)

1 Dipartimento di Matematica [Universita di Brescia]
2 TECHNION - Department of Mathematics

This paper develops the basic analytical theory related to some recently introduced crowd dynamics models. Where well posedness was known only locally in time, it is here extended to all of $\reali^+$. The results on the stability with respect to the equations are improved. Moreover, here the case of several populations is considered, obtaining the well posedness of systems of multi-D non-local conservation laws. The basic analytical tools are provided by the classical Kruzkov theory of scalar conservation laws in several space dimensions.

Mots clés: Hyperbolic conservation laws; nonlocal flow; pedestrian traffic

Domaines: Equations aux dérivées partielles [math.AP]

Rinaldo M. Colombo, Magali Lécureux-Mercier. Nonlocal Crowd Dynamics Models for several Populations. 2011. ⟨hal-00632755⟩