On entropy weak solutions of Hughes’ model for pedestrian motion

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dc.contributor.author El-Khatib, Nader
dc.contributor.author Goatin, Paola
dc.contributor.author Rosini, Massimiliano D.
dc.date.accessioned 2017-01-10T08:08:04Z
dc.date.available 2017-01-10T08:08:04Z
dc.date.copyright 2012 en_US
dc.date.issued 2017-01-10
dc.identifier.issn 0044-2275 en_US
dc.identifier.uri http://hdl.handle.net/10725/5000
dc.description.abstract We consider a generalized version of Hughes’ macroscopic model for crowd motion in the one-dimensional case. It consists in a scalar conservation law accounting for the conservation of the number of pedestrians, coupled with an eikonal equation giving the direction of the flux depending on pedestrian density. As a result of this non-trivial coupling, we have to deal with a conservation law with space–time discontinuous flux, whose discontinuity depends non-locally on the density itself. We propose a definition of entropy weak solution, which allows us to recover a maximum principle. Moreover, we study the structure of the solutions to Riemann-type problems, and we construct them explicitly for small times, depending on the choice of the running cost in the eikonal equation. In particular, aiming at the optimization of the evacuation time, we propose a strategy that is optimal in the case of high densities. All results are illustrated by numerical simulations. en_US
dc.language.iso en en_US
dc.title On entropy weak solutions of Hughes’ model for pedestrian motion en_US
dc.type Article en_US
dc.description.version Published en_US
dc.author.school SAS en_US
dc.author.idnumber 201105930 en_US
dc.author.department Computer Science and Mathematics en_US
dc.description.embargo N/A en_US
dc.relation.journal Zeitschrift für angewandte Mathematik und Physik en_US
dc.journal.volume 64 en_US
dc.journal.issue 2 en_US
dc.article.pages 223-251 en_US
dc.keywords Pedestrian flow en_US
dc.keywords Conservation laws en_US
dc.keywords Eikonal equation en_US
dc.keywords Weak entropy solutions en_US
dc.keywords Numerical approximations en_US
dc.identifier.doi http://dx.doi.org/ 10.1007/s00033-012-0232-x en_US
dc.identifier.ctation El-Khatib, N., Goatin, P., & Rosini, M. D. (2013). On entropy weak solutions of Hughes’ model for pedestrian motion. Zeitschrift für angewandte Mathematik und Physik, 64(2), 223-251. en_US
dc.author.email nader.elkhatib@lau.edu.lb en_US
dc.identifier.tou http://libraries.lau.edu.lb/research/laur/terms-of-use/articles.php en_US
dc.identifier.url http://link.springer.com/article/10.1007/s00033-012-0232-x en_US
dc.author.affiliation Lebanese American University en_US

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