Nonlocal Crowd Dynamics Models for several Populations

TL;DR

This paper extends the analytical theory of crowd dynamics models to global well-posedness, improves stability results, and addresses multiple populations using non-local conservation laws and Kruzhkov theory.

Contribution

It introduces the well-posedness of multi-population non-local conservation law systems and extends existing local results to global in time.

Findings

Global well-posedness of crowd models established

Stability results are improved

Multi-population models are analyzed using Kruzhkov theory

Abstract

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.