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A PDE model for unidirectional flows: stationary profiles and asymptotic behaviour

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. MSC 2020: 34B16, 34E13, 34E15, 35B25, 35B40, 65L11, 76A30.
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https://hal.archives-ouvertes.fr/hal-02981091
Contributor : Gaspard Jankowiak <>
Submitted on : Thursday, December 10, 2020 - 3:36:21 PM
Last modification on : Tuesday, December 15, 2020 - 3:08:02 AM

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  • HAL Id : hal-02981091, version 2

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Annalisa Iuorio, Gaspard Jankowiak, Peter Szmolyan, Marie-Therese Wolfram. A PDE model for unidirectional flows: stationary profiles and asymptotic behaviour. 2020. ⟨hal-02981091v2⟩

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