On the Hughes Model and Numerical Aspects
Analysis of PDEs
2016-05-03 v2 Optimization and Control
Abstract
We study a crowd model proposed by R. Hughes and we describe a numerical approach to solve it. The Hughes model comprises a Fokker-Planck equation coupled with an eikonal equation with Dirichlet or Neumann data. First, we establish a priori estimates for the solutions. Second, we study radial solutions and identify a shock formation mechanism. Third, we illustrate the existence of congestion, the breakdown of the model, and the trend to the equilibrium. Finally, we propose a new numerical method and consider two numerical examples.
Cite
@article{arxiv.1603.06237,
title = {On the Hughes Model and Numerical Aspects},
author = {Diogo A. Gomes and Roberto M. Velho},
journal= {arXiv preprint arXiv:1603.06237},
year = {2016}
}
Comments
12 pages, 17 figures