Semi-Discrete Shocks for a Microscopic Pedestrian Model

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dc.contributor.author Joumaa, Agatha
dc.date.accessioned 2022-10-31T09:51:26Z
dc.date.available 2022-10-31T09:51:26Z
dc.date.copyright 2022 en_US
dc.date.issued 2022-06-20
dc.identifier.uri http://hdl.handle.net/10725/14175
dc.description.abstract In this thesis, we explore in the framework of viscosity solutions the existence and uniqueness of traveling solutions using a pedestrian microscopic model. We consider that the velocity of the pedestrian at position u(y) depends on the velocity of two pedestrians ahead. u′(y) = V (u(y + 1) − u(y)) + V (u(y + 2) − u(y)) Throughout this work, we give the definition of a viscosity solution first then we prove the exponential behavior of the solution at ±∞. After that, using the monotony of the pedestrians interdistance which we achieve by the strong comparison principle, we derive necessarily conditions for the existence of such solutions. With this established, we proceed by constructing a traveling solution considering an approximate non-local operator on a bounded domain and using Perron’s method. en_US
dc.language.iso en en_US
dc.subject Pedestrian traffic flow -- Mathematical models en_US
dc.subject Pedestrian traffic flow -- Methods en_US
dc.subject Viscosity solutions en_US
dc.subject Shock (Mechanics) -- Mathematical models en_US
dc.subject Lebanese American University -- Dissertations en_US
dc.subject Dissertations, Academic en_US
dc.title Semi-Discrete Shocks for a Microscopic Pedestrian Model en_US
dc.type Thesis en_US
dc.term.submitted Summer en_US
dc.author.degree MS in Applied and Computational Mathematics en_US
dc.author.school SAS en_US
dc.author.idnumber 202005236 en_US
dc.author.commembers Nour, Chadi
dc.author.commembers Zaydan, Mamdouh
dc.author.department Computer Science And Mathematics en_US
dc.description.physdesc 1 online resource (viii, 65 leaves) en_US
dc.author.advisor El-Khatib, Nader
dc.keywords Pedestrian traffic en_US
dc.keywords Semi-discrete shocks en_US
dc.keywords Social force model en_US
dc.keywords Strong comparison principle en_US
dc.keywords Viscosity solution en_US
dc.description.bibliographiccitations Bibliography: leaves 62-65. en_US
dc.identifier.doi https://doi.org/10.26756/th.2022.489
dc.author.email agatha.joumaa@lau.edu en_US
dc.identifier.tou http://libraries.lau.edu.lb/research/laur/terms-of-use/thesis.php en_US
dc.publisher.institution Lebanese American University en_US
dc.author.affiliation Lebanese American University en_US

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