2016/12/22 by Sabine Hittmeir, Hittmeir, Sabine, Helene Ranetbauer +5
Engineering · Environmental Science · #Analysis of PDEs (math.AP) #Evacuation and Crowd Dynamics #FOS: Mathematics #Flood Risk Assessment and Management #Traffic control and management
paper · pdf · doi:10.48550/arxiv.1612.07582
openalex publication_date 2016/12/22 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/01
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.