Modeling crowd dynamics through hyperbolic – elliptic equations

Abstract

Inspired by the works of Hughes [22, 23], 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.