Lane formation by side-stepping

Burger M, Hittmeir S, Ranetbauer H, Wolfram MT (2016)

Publication Type: Journal article

Publication year: 2016

Journal

SIAM Journal on Mathematical Analysis Society for Industrial and Applied Mathematics

Publisher: Society for Industrial and Applied Mathematics Publications

Book Volume: 48

Pages Range: 981-1005

Issue: 2

DOI: 10.1137/15M1033174

Abstract

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.

Authors with CRIS profile

Martin Burger

Involved external institutions

Westfälische Wilhelms-Universität (WWU) Münster DE Germany (DE) Österreichische Akademie der Wissenschaften AT Austria (AT)

How to cite

APA:

Burger, M., Hittmeir, S., Ranetbauer, H., & Wolfram, M.-T. (2016). Lane formation by side-stepping. SIAM Journal on Mathematical Analysis, 48, 981-1005. https://doi.org/10.1137/15M1033174

MLA:

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

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