On entropy weak solutions of Hughes’ model for pedestrian motion
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 pedestria...
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2012
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| Online Access: | http://hdl.handle.net/10725/5000 http://dx.doi.org/ 10.1007/s00033-012-0232-x http://libraries.lau.edu.lb/research/laur/terms-of-use/articles.php http://link.springer.com/article/10.1007/s00033-012-0232-x |
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| _version_ | 1864513464961073152 |
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| author | El-Khatib, Nader |
| author2 | Goatin, Paola Rosini, Massimiliano D. |
| author2_role | author author |
| author_facet | El-Khatib, Nader Goatin, Paola Rosini, Massimiliano D. |
| author_role | author |
| dc.creator.none.fl_str_mv | El-Khatib, Nader Goatin, Paola Rosini, Massimiliano D. |
| dc.date.none.fl_str_mv | 2012 2017-01-10T08:08:04Z 2017-01-10T08:08:04Z 2017-01-10 |
| dc.identifier.none.fl_str_mv | 0044-2275 http://hdl.handle.net/10725/5000 http://dx.doi.org/ 10.1007/s00033-012-0232-x 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. http://libraries.lau.edu.lb/research/laur/terms-of-use/articles.php http://link.springer.com/article/10.1007/s00033-012-0232-x |
| dc.language.none.fl_str_mv | en |
| dc.relation.none.fl_str_mv | Zeitschrift für angewandte Mathematik und Physik |
| dc.rights.*.fl_str_mv | info:eu-repo/semantics/openAccess |
| dc.title.none.fl_str_mv | On entropy weak solutions of Hughes’ model for pedestrian motion |
| dc.type.none.fl_str_mv | Article info:eu-repo/semantics/publishedVersion info:eu-repo/semantics/article |
| description | 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. |
| eu_rights_str_mv | openAccess |
| format | article |
| id | LAURepo_5ee85a8f49cbe26c6cb0b7b929ff7bd9 |
| identifier_str_mv | 0044-2275 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. |
| language_invalid_str_mv | en |
| network_acronym_str | LAURepo |
| network_name_str | Lebanese American University repository |
| oai_identifier_str | oai:laur.lau.edu.lb:10725/5000 |
| publishDate | 2012 |
| repository.mail.fl_str_mv | |
| repository.name.fl_str_mv | |
| repository_id_str | |
| spelling | On entropy weak solutions of Hughes’ model for pedestrian motionEl-Khatib, NaderGoatin, PaolaRosini, Massimiliano D.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.PublishedN/A2017-01-10T08:08:04Z2017-01-10T08:08:04Z20122017-01-10Articleinfo:eu-repo/semantics/publishedVersioninfo:eu-repo/semantics/article0044-2275http://hdl.handle.net/10725/5000http://dx.doi.org/ 10.1007/s00033-012-0232-xEl-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.http://libraries.lau.edu.lb/research/laur/terms-of-use/articles.phphttp://link.springer.com/article/10.1007/s00033-012-0232-xenZeitschrift für angewandte Mathematik und Physikinfo:eu-repo/semantics/openAccessoai:laur.lau.edu.lb:10725/50002021-03-19T10:00:53Z |
| spellingShingle | On entropy weak solutions of Hughes’ model for pedestrian motion El-Khatib, Nader |
| status_str | publishedVersion |
| title | On entropy weak solutions of Hughes’ model for pedestrian motion |
| title_full | On entropy weak solutions of Hughes’ model for pedestrian motion |
| title_fullStr | On entropy weak solutions of Hughes’ model for pedestrian motion |
| title_full_unstemmed | On entropy weak solutions of Hughes’ model for pedestrian motion |
| title_short | On entropy weak solutions of Hughes’ model for pedestrian motion |
| title_sort | On entropy weak solutions of Hughes’ model for pedestrian motion |
| url | http://hdl.handle.net/10725/5000 http://dx.doi.org/ 10.1007/s00033-012-0232-x http://libraries.lau.edu.lb/research/laur/terms-of-use/articles.php http://link.springer.com/article/10.1007/s00033-012-0232-x |