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A PDE model for unidirectional flows: stationary profiles and asymptotic behaviour
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Iuorio, Annalisa, Jankowiak, Gaspard, Szmolyan, Peter and Wolfram, Marie-Therese (2022) A PDE model for unidirectional flows: stationary profiles and asymptotic behaviour. Journal of Mathematical Analysis and Applications, 510 (2). 126018. doi:10.1016/j.jmaa.2022.126018 ISSN 0022-247X.
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Official URL: https://doi.org/10.1016/j.jmaa.2022.126018
Abstract
In this paper, we investigate the stationary profiles of a convection-diffusion model for unidirectional pedestrian flows in domains with a single entrance and exit. The inflow and outflow conditions at both the entrance and exit as well as the shape of the domain have a strong influence on the structure of stationary profiles, in particular on the formation of boundary layers. We are able to relate the location and shape of these layers to the inflow and outflow conditions as well as the shape of the domain using geometric singular perturbation theory. Furthermore, we confirm and exemplify our analytical results by means of computational experiments.
| Item Type: | Journal Article | |||||||||
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| Subjects: | Q Science > QA Mathematics | |||||||||
| Divisions: | Faculty of Science, Engineering and Medicine > Science > Mathematics | |||||||||
| Library of Congress Subject Headings (LCSH): | Singular perturbations (Mathematics), Pedestrian traffic flow -- Mathematical models, Boundary value problems | |||||||||
| Journal or Publication Title: | Journal of Mathematical Analysis and Applications | |||||||||
| Publisher: | Academic Press | |||||||||
| ISSN: | 0022-247X | |||||||||
| Official Date: | 15 June 2022 | |||||||||
| Dates: |
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| Volume: | 510 | |||||||||
| Number: | 2 | |||||||||
| Article Number: | 126018 | |||||||||
| DOI: | 10.1016/j.jmaa.2022.126018 | |||||||||
| Status: | Peer Reviewed | |||||||||
| Publication Status: | Published | |||||||||
| Access rights to Published version: | Open Access (Creative Commons) | |||||||||
| Date of first compliant deposit: | 17 January 2022 | |||||||||
| Date of first compliant Open Access: | 2 February 2022 | |||||||||
| RIOXX Funder/Project Grant: |
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