A PDE model for unidirectional flows: stationary profiles and asymptotic behaviour
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arXiv
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| Main Authors: | , , , |
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| Format: | Preprint |
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2020
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| _version_ | 1866915924423999488 |
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| author | Iuorio, Annalisa Jankowiak, Gaspard Szmolyan, Peter Wolfram, Marie-Therese |
| author_facet | Iuorio, Annalisa Jankowiak, Gaspard Szmolyan, Peter Wolfram, Marie-Therese |
| contents | 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. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2010_14424 |
| institution | arXiv |
| publishDate | 2020 |
| record_format | arxiv |
| spellingShingle | A PDE model for unidirectional flows: stationary profiles and asymptotic behaviour Iuorio, Annalisa Jankowiak, Gaspard Szmolyan, Peter Wolfram, Marie-Therese Analysis of PDEs Dynamical Systems 34B16, 34E13 (Primary) 34E15, 35B25, 35B40, 65L11, 76A30 (Secondary) 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. |
| title | A PDE model for unidirectional flows: stationary profiles and asymptotic behaviour |
| topic | Analysis of PDEs Dynamical Systems 34B16, 34E13 (Primary) 34E15, 35B25, 35B40, 65L11, 76A30 (Secondary) |
| url | https://arxiv.org/abs/2010.14424 |