Derivation and analysis of continuum models for crossing pedestrian   traffic
  In this paper we study hyperbolic and parabolic nonlinear partial differential equation models, which describe the evolution of two intersecting pedestrian flows. We assume that individuals avoid collisions by sidestepping, which is encoded in the transition rates of the microscopic 2D model. We formally derive the corresponding mean-field models and prove existence of global weak solutions for the parabolic model. Moreover we discuss stability of stationary states for the corresponding one-dimensional model. Furthermore we illustrate the rich dynamics of both systems with numerical simulations. 
Sabine Hittmeir, Helene Ranetbauer, Christian Schmeiser, Marie-Therese   Wolfram
math.AP