A PDE model for unidirectional flows: stationary profiles and asymptotic behaviour - Archive ouverte HAL Access content directly
Preprints, Working Papers, ... Year : 2020

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.
Fichier principal
Vignette du fichier
ms.pdf (1.3 Mo) Télécharger le fichier
Origin Files produced by the author(s)

Dates and versions

hal-02981091 , version 1 (27-10-2020)
hal-02981091 , version 2 (10-12-2020)

Identifiers

  • HAL Id : hal-02981091 , version 2

Cite

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

Collections

TDS-MACS
45 View
52 Download

Share

Gmail Mastodon Facebook X LinkedIn More