On the Hughes model and numerical aspects

Handle URI:
http://hdl.handle.net/10754/622731
Title:
On the Hughes model and numerical aspects
Authors:
Gomes, Diogo A. ( 0000-0002-3129-3956 ) ; Machado Velho, Roberto
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.
KAUST Department:
Center for Uncertainty Quantification in Computational Science and Engineering (SRI-UQ); Computer, Electrical and Mathematical Sciences and Engineering (CEMSE) Division
Citation:
Gomes 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.
Publisher:
Institute of Electrical and Electronics Engineers (IEEE)
Journal:
2016 IEEE 55th Conference on Decision and Control (CDC)
Issue Date:
5-Jan-2017
DOI:
10.1109/CDC.2016.7798683
ARXIV:
arXiv:1603.06237
Type:
Conference Paper
Sponsors:
This work was partially supported by KAUST baseline and start-up funds and KAUST SRI, Uncertainty Quantification Center in Computational Science and Engineering
Additional Links:
http://ieeexplore.ieee.org/document/7798683/
Appears in Collections:
Conference Papers; Computer, Electrical and Mathematical Sciences and Engineering (CEMSE) Division

Full metadata record

DC FieldValue Language
dc.contributor.authorGomes, Diogo A.en
dc.contributor.authorMachado Velho, Robertoen
dc.date.accessioned2017-01-25T10:37:00Z-
dc.date.available2017-01-25T10:37:00Z-
dc.date.issued2017-01-05en
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.en
dc.identifier.doi10.1109/CDC.2016.7798683en
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.en
dc.description.sponsorshipThis work was partially supported by KAUST baseline and start-up funds and KAUST SRI, Uncertainty Quantification Center in Computational Science and Engineeringen
dc.publisherInstitute of Electrical and Electronics Engineers (IEEE)en
dc.relation.urlhttp://ieeexplore.ieee.org/document/7798683/en
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.en
dc.subjectBoundary conditionsen
dc.subjectElectric breakdownen
dc.subjectElectric shocken
dc.subjectMarket researchen
dc.subjectMathematical modelen
dc.subjectNumerical modelsen
dc.subjectViscosityen
dc.titleOn the Hughes model and numerical aspectsen
dc.typeConference Paperen
dc.contributor.departmentCenter for Uncertainty Quantification in Computational Science and Engineering (SRI-UQ)en
dc.contributor.departmentComputer, Electrical and Mathematical Sciences and Engineering (CEMSE) Divisionen
dc.identifier.journal2016 IEEE 55th Conference on Decision and Control (CDC)en
dc.eprint.versionPost-printen
dc.identifier.arxividarXiv:1603.06237en
kaust.authorGomes, Diogo A.en
kaust.authorMachado Velho, Robertoen
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