Lane formation by side-stepping

Beitrag in einer Fachzeitschrift


Details zur Publikation

Autorinnen und Autoren: Burger M, Hittmeir S, Ranetbauer H, Wolfram MT
Zeitschrift: SIAM Journal on Mathematical Analysis
Verlag: Society for Industrial and Applied Mathematics Publications
Jahr der Veröffentlichung: 2016
Band: 48
Seitenbereich: 981-1005
ISSN: 0036-1410


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.


Einrichtungen weiterer Autorinnen und Autoren

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


Zitierweisen

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://dx.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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