TY - JOUR
T1 - Mean field games with nonlinear mobilities in pedestrian dynamics
AU - Burger, Martin
AU - Di Francesco, Marco
AU - Markowich, Peter A.
AU - Wolfram, Marie Therese
N1 - KAUST Repository Item: Exported on 2020-10-01
Acknowledgements: MTW acknowledges financial support of the Austrian Science Foundation FWF via the Hertha Firnberg Project T456-N23. MDF is supported by the FP7-People Marie Curie CIG (Career Integration Grant) Diffusive Partial Differential Equations with Nonlocal Interaction in Biology and Social Sciences (DifNonLoc), by the 'Ramon y Cajal' sub-programme (MICINN-RYC) of the Spanish Ministry of Science and Innovation, Ref. RYC-2010-06412, and by the by the Ministerio de Ciencia e Innovacion, grant MTM2011-27739-C04-02. The authors thank the anonymous referees for useful comments to improve the manuscript.
PY - 2014/4
Y1 - 2014/4
N2 - In this paper we present an optimal control approach modeling fast exit scenarios in pedestrian crowds. In particular we consider the case of a large human crowd trying to exit a room as fast as possible. The motion of every pedestrian is determined by minimizing a cost functional, which depends on his/her position, velocity, exit time and the overall density of people. This microscopic setup leads in the mean-field limit to a parabolic optimal control problem. We discuss the modeling of the macroscopic optimal control approach and show how the optimal conditions relate to the Hughes model for pedestrian flow. Furthermore we provide results on the existence and uniqueness of minimizers and illustrate the behavior of the model with various numerical results.
AB - In this paper we present an optimal control approach modeling fast exit scenarios in pedestrian crowds. In particular we consider the case of a large human crowd trying to exit a room as fast as possible. The motion of every pedestrian is determined by minimizing a cost functional, which depends on his/her position, velocity, exit time and the overall density of people. This microscopic setup leads in the mean-field limit to a parabolic optimal control problem. We discuss the modeling of the macroscopic optimal control approach and show how the optimal conditions relate to the Hughes model for pedestrian flow. Furthermore we provide results on the existence and uniqueness of minimizers and illustrate the behavior of the model with various numerical results.
UR - http://hdl.handle.net/10754/564890
UR - http://arxiv.org/abs/arXiv:1304.5201v1
UR - http://www.scopus.com/inward/record.url?scp=84902192859&partnerID=8YFLogxK
U2 - 10.3934/dcdsb.2014.19.1311
DO - 10.3934/dcdsb.2014.19.1311
M3 - Article
VL - 19
SP - 1311
EP - 1333
JO - Discrete and Continuous Dynamical Systems - Series B
JF - Discrete and Continuous Dynamical Systems - Series B
SN - 1531-3492
IS - 5
ER -