A PDE model for unidirectional flows: stationary profiles and asymptotic behaviour
Analysis of PDEs
2026-04-10 v2 Dynamical Systems
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.
Cite
@article{arxiv.2010.14424,
title = {A PDE model for unidirectional flows: stationary profiles and asymptotic behaviour},
author = {Annalisa Iuorio and Gaspard Jankowiak and Peter Szmolyan and Marie-Therese Wolfram},
journal= {arXiv preprint arXiv:2010.14424},
year = {2026}
}
Comments
35 pages