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dc.contributor.authorGomes, Diogo A.
dc.contributor.authorMachado Velho, Roberto
dc.date.accessioned2017-01-25T10:37:00Z
dc.date.available2017-01-25T10:37:00Z
dc.date.issued2017-01-05
dc.identifier.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.
dc.identifier.doi10.1109/CDC.2016.7798683
dc.identifier.urihttp://hdl.handle.net/10754/622731
dc.description.abstractWe 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.
dc.description.sponsorshipThis work was partially supported by KAUST baseline and start-up funds and KAUST SRI, Uncertainty Quantification Center in Computational Science and Engineering
dc.publisherInstitute of Electrical and Electronics Engineers (IEEE)
dc.relation.urlhttp://ieeexplore.ieee.org/document/7798683/
dc.rights(c) 2016 IEEE. Personal use of this material is permitted. Permission from IEEE must be obtained for all other users, including reprinting/ republishing this material for advertising or promotional purposes, creating new collective works for resale or redistribution to servers or lists, or reuse of any copyrighted components of this work in other works.
dc.subjectBoundary conditions
dc.subjectElectric breakdown
dc.subjectElectric shock
dc.subjectMarket research
dc.subjectMathematical model
dc.subjectNumerical models
dc.subjectViscosity
dc.titleOn the Hughes model and numerical aspects
dc.typeConference Paper
dc.contributor.departmentCenter for Uncertainty Quantification in Computational Science and Engineering (SRI-UQ)
dc.contributor.departmentComputer, Electrical and Mathematical Sciences and Engineering (CEMSE) Division
dc.identifier.journal2016 IEEE 55th Conference on Decision and Control (CDC)
dc.eprint.versionPost-print
dc.identifier.arxividarXiv:1603.06237
kaust.personGomes, Diogo A.
kaust.personMachado Velho, Roberto
refterms.dateFOA2018-06-13T14:59:36Z


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