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dc.contributor.authorDi Francesco, Marco
dc.contributor.authorMarkowich, Peter A.
dc.contributor.authorPietschmann, Jan-Frederik
dc.contributor.authorWolfram, Marie-Therese
dc.date.accessioned2016-02-25T13:52:01Z
dc.date.available2016-02-25T13:52:01Z
dc.date.issued2011-02
dc.identifier.citationDi Francesco M, Markowich PA, Pietschmann J-F, Wolfram M-T (2011) On the Hughes’ model for pedestrian flow: The one-dimensional case. Journal of Differential Equations 250: 1334–1362. Available: http://dx.doi.org/10.1016/j.jde.2010.10.015.
dc.identifier.issn0022-0396
dc.identifier.doi10.1016/j.jde.2010.10.015
dc.identifier.urihttp://hdl.handle.net/10754/599056
dc.description.abstractIn this paper we investigate the mathematical theory of Hughes' model for the flow of pedestrians (cf. Hughes (2002) [17]), consisting of a non-linear conservation law for the density of pedestrians coupled with an eikonal equation for a potential modelling the common sense of the task. For such an approximated system we prove existence and uniqueness of entropy solutions (in one space dimension) in the sense of Kružkov (1970) [22], in which the boundary conditions are posed following the approach of Bardos et al. (1979) [7]. We use BV estimates on the density ρ and stability estimates on the potential Π in order to prove uniqueness. Furthermore, we analyze the evolution of characteristics for the original Hughes' model in one space dimension and study the behavior of simple solutions, in order to reproduce interesting phenomena related to the formation of shocks and rarefaction waves. The characteristic calculus is supported by numerical simulations. © 2010 Elsevier Inc.
dc.description.sponsorshipThis publication is based on work supported by Award No. KUK-I1-007-43, made by King Abdullah University of Science and Technology (KAUST), by the Leverhulme Trust through the research grant entitled Kinetic and mean field partial differential models for socio-economic processes (PI Peter Markowich) and by the Royal Society through the Wolfson Research Merit Award of Peter Markowich. PM is also grateful to the Humboldt foundation for their support. MDF is partially supported by the Italian MIUR under the PRIN program 'Nonlinear Systems of Conservation Laws and Fluid Dynamics'. Furthermore, the authors thank Martin Burger and the Institute for Computational and Applied Mathematics at the University of Munster for their kind hospitality and stimulating discussions.
dc.publisherElsevier BV
dc.subjectCharacteristics
dc.subjectEikonal equation
dc.subjectElliptic coupling
dc.subjectEntropy solutions
dc.subjectPedestrian flow
dc.subjectScalar conservation laws
dc.titleOn the Hughes' model for pedestrian flow: The one-dimensional case
dc.typeArticle
dc.identifier.journalJournal of Differential Equations
dc.contributor.institutionUniversita degli Studi dell'Aquila, L'Aquila, Italy
dc.contributor.institutionUniversity of Cambridge, Cambridge, United Kingdom
dc.contributor.institutionUniversitat Wien, Vienna, Austria
kaust.grant.numberKUK-I1-007-43


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