Modeling Crowd Dynamics through Hyperbolic - Elliptic Equations
  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. 
Rinaldo M. Colombo and Maria Gokieli and Massimiliano D. Rosini
math.AP