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    Mean field games with nonlinear mobilities in pedestrian dynamics

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    Type
    Conference Paper
    Authors
    Burger, Martin
    Francesco, Marco Di
    Markowich, Peter A.
    Wolfram, Marie-Therese
    KAUST Department
    Applied Mathematics and Computational Science Program
    Computer, Electrical and Mathematical Sciences and Engineering (CEMSE) Division
    Date
    2014
    Preprint Posting Date
    2013-04-18
    Permanent link to this record
    http://hdl.handle.net/10754/564890
    
    Metadata
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    Abstract
    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.2014.19.1311
    Sponsors
    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.
    Publisher
    American Institute of Mathematical Sciences (AIMS)
    Journal
    Discrete and Continuous Dynamical Systems - Series B
    DOI
    10.3934/dcdsb.2014.19.1311
    arXiv
    1304.5201
    Additional Links
    http://aimsciences.org//article/doi/10.3934/dcdsb.2014.19.1311
    http://arxiv.org/pdf/1304.5201
    ae974a485f413a2113503eed53cd6c53
    10.3934/dcdsb.2014.19.1311
    Scopus Count
    Collections
    Articles; Applied Mathematics and Computational Science Program; Computer, Electrical and Mathematical Science and Engineering (CEMSE) Division

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