Mean field games with nonlinear mobilities in pedestrian dynamics
Type
Conference PaperKAUST Department
Applied Mathematics and Computational Science ProgramComputer, Electrical and Mathematical Sciences and Engineering (CEMSE) Division
Date
2014Preprint Posting Date
2013-04-18Permanent link to this record
http://hdl.handle.net/10754/564890
Metadata
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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.Citation
Burger, M., Di Francesco, M., A. Markowich, P., … Wolfram, M.-T. (2014). Mean field games with nonlinear mobilities in pedestrian dynamics. Discrete & Continuous Dynamical Systems - B, 19(5), 1311–1333. doi:10.3934/dcdsb.2014.19.1311Sponsors
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.arXiv
1304.5201Additional Links
http://aimsciences.org//article/doi/10.3934/dcdsb.2014.19.1311http://arxiv.org/pdf/1304.5201
ae974a485f413a2113503eed53cd6c53
10.3934/dcdsb.2014.19.1311