Short-time existence of solutions for mean-field games with congestion

Handle URI:
http://hdl.handle.net/10754/595341
Title:
Short-time existence of solutions for mean-field games with congestion
Authors:
Gomes, Diogo A. ( 0000-0002-3129-3956 ) ; Voskanyan, Vardan K.
Abstract:
We consider time-dependent mean-field games with congestion that are given by a Hamilton–Jacobi equation coupled with a Fokker–Planck equation. These models are motivated by crowd dynamics in which agents have difficulty moving in high-density areas. The congestion effects make the Hamilton–Jacobi equation singular. The uniqueness of solutions for this problem is well understood; however, the existence of classical solutions was only known in very special cases, stationary problems with quadratic Hamiltonians and some time-dependent explicit examples. Here, we demonstrate the short-time existence of C∞ solutions for sub-quadratic Hamiltonians.
KAUST Department:
Computer, Electrical and Mathematical Sciences and Engineering (CEMSE) Division; Center for Uncertainty Quantification in Computational Science and Engineering (SRI-UQ)
Citation:
Short-time existence of solutions for mean-field games with congestion 2015, 92 (3):778 Journal of the London Mathematical Society
Publisher:
Oxford University Press (OUP)
Journal:
Journal of the London Mathematical Society
Issue Date:
20-Nov-2015
DOI:
10.1112/jlms/jdv052
Type:
Article
ISSN:
0024-6107; 1469-7750
Additional Links:
http://jlms.oxfordjournals.org/lookup/doi/10.1112/jlms/jdv052
Appears in Collections:
Articles; Computer, Electrical and Mathematical Sciences and Engineering (CEMSE) Division

Full metadata record

DC FieldValue Language
dc.contributor.authorGomes, Diogo A.en
dc.contributor.authorVoskanyan, Vardan K.en
dc.date.accessioned2016-02-01T12:41:38Zen
dc.date.available2016-02-01T12:41:38Zen
dc.date.issued2015-11-20en
dc.identifier.citationShort-time existence of solutions for mean-field games with congestion 2015, 92 (3):778 Journal of the London Mathematical Societyen
dc.identifier.issn0024-6107en
dc.identifier.issn1469-7750en
dc.identifier.doi10.1112/jlms/jdv052en
dc.identifier.urihttp://hdl.handle.net/10754/595341en
dc.description.abstractWe consider time-dependent mean-field games with congestion that are given by a Hamilton–Jacobi equation coupled with a Fokker–Planck equation. These models are motivated by crowd dynamics in which agents have difficulty moving in high-density areas. The congestion effects make the Hamilton–Jacobi equation singular. The uniqueness of solutions for this problem is well understood; however, the existence of classical solutions was only known in very special cases, stationary problems with quadratic Hamiltonians and some time-dependent explicit examples. Here, we demonstrate the short-time existence of C∞ solutions for sub-quadratic Hamiltonians.en
dc.language.isoenen
dc.publisherOxford University Press (OUP)en
dc.relation.urlhttp://jlms.oxfordjournals.org/lookup/doi/10.1112/jlms/jdv052en
dc.rightsThis is a pre-copyedited, author-produced PDF of an article accepted for publication in Journal of the London Mathematical Society following peer review. The version of record is available online at: http://jlms.oxfordjournals.org/lookup/doi/10.1112/jlms/jdv052.en
dc.titleShort-time existence of solutions for mean-field games with congestionen
dc.typeArticleen
dc.contributor.departmentComputer, Electrical and Mathematical Sciences and Engineering (CEMSE) Divisionen
dc.contributor.departmentCenter for Uncertainty Quantification in Computational Science and Engineering (SRI-UQ)en
dc.identifier.journalJournal of the London Mathematical Societyen
dc.eprint.versionPost-printen
dc.contributor.affiliationKing Abdullah University of Science and Technology (KAUST)en
kaust.authorGomes, Diogo A.en
kaust.authorVoskanyan, Vardan K.en
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