KAUST DepartmentApplied Mathematics and Computational Science Program
Center for Uncertainty Quantification in Computational Science and Engineering (SRI-UQ)
Computer, Electrical and Mathematical Sciences and Engineering (CEMSE) Division
Preprint Posting Date2016-03-20
Online Publication Date2017-01-05
Print Publication Date2016-12
Permanent link to this recordhttp://hdl.handle.net/10754/622731
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AbstractWe study a crowd model proposed by R. Hughes in  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.
CitationGomes DA, Velho RM (2016) On the Hughes model and numerical aspects. 2016 IEEE 55th Conference on Decision and Control (CDC). Available: http://dx.doi.org/10.1109/CDC.2016.7798683.
SponsorsThis work was partially supported by KAUST baseline and start-up funds and KAUST SRI, Uncertainty Quantification Center in Computational Science and Engineering