Show simple item record

dc.contributor.authorBurger, Martin
dc.contributor.authorDi Francesco, Marco
dc.contributor.authorMarkowich, Peter A.
dc.contributor.authorWolfram, Marie Therese
dc.date.accessioned2015-08-04T07:24:15Z
dc.date.available2015-08-04T07:24:15Z
dc.date.issued2014-04
dc.identifier.issn15313492
dc.identifier.doi10.3934/dcdsb.2014.19.1311
dc.identifier.urihttp://hdl.handle.net/10754/564890
dc.description.abstractIn 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.
dc.description.sponsorshipMTW 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.
dc.publisherAmerican Institute of Mathematical Sciences (AIMS)
dc.relation.urlhttp://arxiv.org/abs/arXiv:1304.5201v1
dc.subjectCalculus of variations
dc.subjectMean field limit
dc.subjectNumerical simulations
dc.subjectOptimal control
dc.subjectPedestrian dynamics
dc.titleMean field games with nonlinear mobilities in pedestrian dynamics
dc.typeArticle
dc.contributor.departmentApplied Mathematics and Computational Science Program
dc.contributor.departmentComputer, Electrical and Mathematical Sciences and Engineering (CEMSE) Division
dc.identifier.journalDiscrete and Continuous Dynamical Systems - Series B
dc.contributor.institutionInstitute for Computational and Applied Mathematics, University of Münster, Einsteinstrasse 62, 48149 Münstar, Germany
dc.contributor.institutionDepartment of Mathematical Sciences, University of Bath, 4W, 1.14, Claverton Down, Bath, BA2 7AY, United Kingdom
dc.contributor.institutionDepartment of Mathematics, University of Vienna, Nordbergstrasse 15, 1090 Vienna, Austria
dc.identifier.arxividarXiv:1304.5201
kaust.personMarkowich, Peter A.
dc.versionv1
dc.date.posted2013-04-18


This item appears in the following Collection(s)

Show simple item record