Lane formation by side-stepping

Journal article

Publication Details

Author(s): Burger M, Hittmeir S, Ranetbauer H, Wolfram MT
Journal: SIAM Journal on Mathematical Analysis
Publisher: Society for Industrial and Applied Mathematics Publications
Publication year: 2016
Volume: 48
Pages range: 981-1005
ISSN: 0036-1410


In this paper we study a system of nonlinear partial differential equations, which describes the evolution of two pedestrian groups moving in opposite directions. The pedestrian dynamics are driven by aversion and cohesion, i.e., the tendency to follow individuals from their own group and step aside in the case of contraow. We start with a two-dimensional lattice-based approach, in which the transition rates reect the described dynamics, and derive the corresponding PDE system by formally passing to the limit in the spatial and temporal discretization. We discuss the existence of special stationary solutions, which correspond to the formation of directional lanes and prove existence of global in time bounded weak solutions. The proof is based on an approximation argument and entropy inequalities. Furthermore, we illustrate the behavior of the system with numerical simulations.

External institutions with authors

Österreichische Akademie der Wissenschaften
Westfälische Wilhelms-Universität (WWU) Münster

How to cite

Burger, M., Hittmeir, S., Ranetbauer, H., & Wolfram, M.-T. (2016). Lane formation by side-stepping. SIAM Journal on Mathematical Analysis, 48, 981-1005.

Burger, Martin, et al. "Lane formation by side-stepping." SIAM Journal on Mathematical Analysis 48 (2016): 981-1005.


Last updated on 2018-03-12 at 09:08