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dc.contributor.authorFerreira, Rita
dc.contributor.authorGomes, Diogo A.
dc.contributor.authorTada, Teruo
dc.date.accessioned2021-07-01T06:42:01Z
dc.date.available2020-02-25T11:05:37Z
dc.date.available2021-07-01T06:42:01Z
dc.date.issued2021-06-30
dc.date.submitted2020-12-03
dc.identifier.citationFerreira, R., Gomes, D., & Tada, T. (2021). Existence of weak solutions to time-dependent mean-field games. Nonlinear Analysis, 212, 112470. doi:10.1016/j.na.2021.112470
dc.identifier.issn0362-546X
dc.identifier.doi10.1016/j.na.2021.112470
dc.identifier.urihttp://hdl.handle.net/10754/661683
dc.description.abstractHere, we establish the existence of weak solutions to a wide class of time-dependent monotone mean-field games (MFGs). These MFGs are given as a system of degenerate parabolic equations with initial and terminal conditions. To construct these solutions, we consider a high-order elliptic regularization in space–time. Then, applying Schaefer’s fixed-point theorem, we obtain the existence and uniqueness for this regularized problem. Using Minty’s method, we prove the existence of a weak solution to the original MFG. Finally, the paper ends with a discussion on congestion problems and density constrained MFGs.
dc.publisherElsevier BV
dc.relation.urlhttps://linkinghub.elsevier.com/retrieve/pii/S0362546X21001450
dc.rightsNOTICE: this is the author’s version of a work that was accepted for publication in Nonlinear Analysis. Changes resulting from the publishing process, such as peer review, editing, corrections, structural formatting, and other quality control mechanisms may not be reflected in this document. Changes may have been made to this work since it was submitted for publication. A definitive version was subsequently published in Nonlinear Analysis, [212, , (2021-06-30)] DOI: 10.1016/j.na.2021.112470 . © 2021. This manuscript version is made available under the CC-BY-NC-ND 4.0 license http://creativecommons.org/licenses/by-nc-nd/4.0/
dc.titleExistence of weak solutions to time-dependent mean-field games
dc.typeArticle
dc.contributor.departmentComputer, Electrical and Mathematical Sciences and Engineering (CEMSE) Division
dc.contributor.departmentApplied Mathematics and Computational Science Program
dc.identifier.journalNonlinear Analysis
dc.rights.embargodate2023-06-30
dc.eprint.versionPost-print
dc.identifier.volume212
dc.identifier.pages112470
dc.identifier.arxivid2001.03928
kaust.personFerreira, Rita
kaust.personGomes, Diogo A.
kaust.personTada, Teruo
dc.date.accepted2021-06-11
refterms.dateFOA2020-02-25T11:05:57Z
dc.date.published-online2021-06-30
dc.date.published-print2021-11
dc.date.posted2020-01-12


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