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Lane formation by side-stepping
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Burger, Martin, Hittmeir, Sabine, Ranetbauer, Helene and Wolfram, Marie-Therese (2016) Lane formation by side-stepping. SIAM Journal on Mathematical Analysis, 48 (2). pp. 981-1005. doi:10.1137/15M1033174 ISSN 0036-1410.
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Official URL: http://dx.doi.org/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 contraflow. We start with a two-dimensional lattice-based approach, in which the transition rates reflect 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.
Item Type: | Journal Article | ||||||
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Subjects: | Q Science > QA Mathematics | ||||||
Divisions: | Faculty of Science, Engineering and Medicine > Science > Mathematics | ||||||
Library of Congress Subject Headings (LCSH): | Differential equations, Partial , Diffusion | ||||||
Journal or Publication Title: | SIAM Journal on Mathematical Analysis | ||||||
Publisher: | Society for Industrial and Applied Mathematics | ||||||
ISSN: | 0036-1410 | ||||||
Official Date: | 15 March 2016 | ||||||
Dates: |
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Volume: | 48 | ||||||
Number: | 2 | ||||||
Page Range: | pp. 981-1005 | ||||||
DOI: | 10.1137/15M1033174 | ||||||
Status: | Peer Reviewed | ||||||
Publication Status: | Published | ||||||
Access rights to Published version: | Restricted or Subscription Access | ||||||
Date of first compliant deposit: | 15 September 2016 | ||||||
Date of first compliant Open Access: | 16 September 2016 |
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