Modeling Crowd Dynamics through Hyperbolic - Elliptic Equations

TL;DR

This paper develops a mathematically rigorous hyperbolic-elliptic model for crowd dynamics, demonstrating well-posedness and finite evacuation times, while capturing individual behaviors within crowds.

Contribution

It formalizes and proves the well-posedness of a novel hyperbolic-elliptic system for crowd movement modeling, linking macroscopic and microscopic descriptions.

Findings

Model is well posed and mathematically sound.

Evacuation time from bounded environments is finite.

Provides a microscopic perspective on individual behaviors.

Abstract

Inspired by the works of Hughes [17, 18], we formalize and prove the well posedness of a hyperbolic--elliptic system whose solutions describe the dynamics of a moving crowd. The resulting model is here shown to be well posed and the time of evacuation from a bounded environment is proved to be finite. This model also provides a microscopic description of the individuals' behaviors.