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In this paper we study hyperbolic and parabolic nonlinear partialdifferential equation models, which describe the evolution of two intersectingpedestrian flows. We assume that individuals avoid collisions by sidestepping,which is encoded in the transition rates of the microscopic 2D model. Weformally derive the corresponding mean-field models and prove existence ofglobal weak solutions for the parabolic model. Moreover we discuss stability ofstationary states for the corresponding one-dimensional model. Furthermore weillustrate the rich dynamics of both systems with numerical simulations.

Derivation and analysis of continuum models for crossing pedestrian traffic