Iuorio, A., Jankowiak, G., Szmolyan, P., & Wolfram, M.-T. (2022). A PDE model for unidirectional flows: Stationary profiles and asymptotic behaviour. Journal of Mathematical Analysis and Applications, 510(2), Article 126018. https://doi.org/10.1016/j.jmaa.2022.126018
Burgers' equation; Dimension reduction; Geometric singular perturbation theory; Non linear boundary value problem; Pedestrian dynamics; Stationary states
en
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.
en
Project (external):
ÖAW FWF
-
Project ID:
NST-0001 T 1199-N
-
Research Areas:
Mathematical and Algorithmic Foundations: 70% Modeling and Simulation: 30%
