On the Hughes model and numerical aspects

Diogo A. Gomes, Roberto Machado Velho

Research output: Chapter in Book/Report/Conference proceedingConference contribution

1 Scopus citations

Abstract

We study a crowd model proposed by R. Hughes in [11] and we describe a numerical approach to solve it. This 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 examples.
Original languageEnglish (US)
Title of host publication2016 IEEE 55th Conference on Decision and Control (CDC)
PublisherInstitute of Electrical and Electronics Engineers (IEEE)
Pages2783-2788
Number of pages6
ISBN (Print)9781509018376
DOIs
StatePublished - Jan 5 2017

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