Modeling and simulation of free boundary problems for crowd dynamics by the kinetic theory for active particles

KNOPOFF DAMIAN; NICOLA BELLOMO

SAN DIEGO

Conferencia; Advances in Computational Mechanics (A Conference Celebrating the 70th Birthday of Thomas Hughes); 2013

This presentation deals with the kinetic theory modeling 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 treated by finite difference methods for hyperbolic equations. Some preliminary reasonings toward the modeling of panic conditions are proposed.