A kinetic approach to the modeling of crowd dynamics

KNOPOFF DAMIAN

BOLOGNA

Workshop; SisCO-SIMAI Workshop: Safety, panic, traffic and crowd dynamics; 2013

p, li { white-space: pre-wrapOm IIIn this presentation we apply the kinetic theory to the modeling of crowd dynamics with the aim of showing how the dynamics at the micro-scale is transferred to the dynamics of collective behaviors. The derivation of a new model is followed by a qualitative analysis of the initial value problem. Existence of solutions is proved for arbitrary large times, while simulations are developed by computational schemes based on splitting methods, where the transport equations are treated by finite difference methods for hyperbolic equations. Some preliminary reasonings toward the modeling of panic conditions are proposed.