{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,6,19]],"date-time":"2025-06-19T08:10:10Z","timestamp":1750320610282,"version":"3.41.0"},"reference-count":64,"publisher":"Society for Industrial & Applied Mathematics (SIAM)","issue":"3","funder":[{"DOI":"10.13039\/100000001","name":"National Science Foundation","doi-asserted-by":"publisher","award":["DMS-2206038"],"award-info":[{"award-number":["DMS-2206038"]}],"id":[{"id":"10.13039\/100000001","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/100006474","name":"Columbia University","doi-asserted-by":"publisher","id":[{"id":"10.13039\/100006474","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/100000001","name":"National Science Foundation","doi-asserted-by":"publisher","award":["DMS-2440215"],"award-info":[{"award-number":["DMS-2440215"]}],"id":[{"id":"10.13039\/100000001","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/100000893","name":"Simons Foundation","doi-asserted-by":"publisher","award":["MPS-TSM-00007305"],"award-info":[{"award-number":["MPS-TSM-00007305"]}],"id":[{"id":"10.13039\/100000893","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/100007579","name":"Auburn University","doi-asserted-by":"publisher","id":[{"id":"10.13039\/100007579","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["SIAM J. Math. Anal."],"published-print":{"date-parts":[[2025,6,30]]},"DOI":"10.1137\/24m1640008","type":"journal-article","created":{"date-parts":[[2025,6,19]],"date-time":"2025-06-19T07:34:02Z","timestamp":1750318442000},"page":"3217-3254","source":"Crossref","is-referenced-by-count":0,"title":["The Convergence Rate of Vanishing Viscosity Approximations for Mean Field Games"],"prefix":"10.1137","volume":"57","author":[{"ORCID":"https:\/\/orcid.org\/0000-0001-7228-1954","authenticated-orcid":true,"given":"Wenpin","family":"Tang","sequence":"first","affiliation":[{"name":"Department of Industrial Engineering and Operations Research, Columbia University, New York, NY 10027 USA."}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-2371-6840","authenticated-orcid":true,"given":"Yuming Paul","family":"Zhang","sequence":"additional","affiliation":[{"name":"Department of Mathematics and Statistics, Auburn University, Auburn, AL 36849 USA."}]}],"member":"351","published-online":{"date-parts":[[2025,6,19]]},"reference":[{"key":"ref2","doi-asserted-by":"publisher","DOI":"10.1137\/090758477"},{"key":"ref3","doi-asserted-by":"publisher","DOI":"10.1007\/978-3-030-59837-2_4"},{"key":"ref4","doi-asserted-by":"publisher","DOI":"10.1007\/s00208-014-1088-5"},{"key":"ref5","doi-asserted-by":"publisher","DOI":"10.4007\/annals.2005.161.223"},{"key":"ref6","doi-asserted-by":"publisher","DOI":"10.1002\/(SICI)1097-0312(199904)52:4<411::AID-CPA1>3.0.CO;2-3"},{"key":"ref7","doi-asserted-by":"publisher","DOI":"10.1137\/120869249"},{"key":"ref8","doi-asserted-by":"publisher","DOI":"10.1002\/cpa.20030"},{"key":"ref9","doi-asserted-by":"publisher","DOI":"10.1051\/cocv\/2021081"},{"key":"ref10","doi-asserted-by":"publisher","DOI":"10.1016\/j.ifacol.2022.11.087"},{"key":"ref11","doi-asserted-by":"publisher","DOI":"10.1016\/j.jmaa.2022.126138"},{"key":"ref12","doi-asserted-by":"publisher","DOI":"10.1007\/978-3-030-01947-1_3"},{"key":"ref13","volume-title":"progress in Nonlinear Differential Equations and their Applications 58","author":"Cannarsa P.","year":"2004"},{"key":"ref14","doi-asserted-by":"publisher","DOI":"10.1214\/17-AAP1276"},{"key":"ref16","doi-asserted-by":"publisher","DOI":"10.1007\/978-3-319-06917-3_5"},{"key":"ref17","doi-asserted-by":"publisher","DOI":"10.1051\/cocv\/2014044"},{"key":"ref18","doi-asserted-by":"publisher","DOI":"10.1007\/s00030-015-0323-4"},{"key":"ref19","doi-asserted-by":"publisher","DOI":"10.3934\/nhm.2012.7.279"},{"key":"ref20","doi-asserted-by":"publisher","DOI":"10.1090\/psapm\/078\/05"},{"key":"ref21","doi-asserted-by":"publisher","DOI":"10.1214\/19-AOP1382"},{"key":"ref22","doi-asserted-by":"publisher","DOI":"10.1142\/S2010326311300014"},{"key":"ref23","doi-asserted-by":"publisher","DOI":"10.1090\/S0025-5718-1984-0744921-8"},{"key":"ref24","doi-asserted-by":"publisher","DOI":"10.1007\/978-1-4612-0895-2"},{"key":"ref25","doi-asserted-by":"publisher","DOI":"10.3934\/ElectrEng.2017.1.18"},{"key":"ref26","doi-asserted-by":"publisher","DOI":"10.1007\/s00205-010-0307-9"},{"key":"ref27","doi-asserted-by":"publisher","DOI":"10.1016\/j.na.2021.112470"},{"key":"ref28","doi-asserted-by":"publisher","DOI":"10.3934\/dcds.2022078"},{"key":"ref29","first-page":"1815","volume":"24","author":"Fetecau R. C.","year":"2019","journal-title":"Discrete Contin. Dyn. Syst. Ser. B"},{"key":"ref30","doi-asserted-by":"publisher","DOI":"10.1007\/s00440-022-01185-2"},{"key":"ref31","doi-asserted-by":"publisher","DOI":"10.1051\/cocv\/2015029"},{"key":"ref32","doi-asserted-by":"publisher","DOI":"10.1080\/03605302.2014.903574"},{"key":"ref33","doi-asserted-by":"publisher","DOI":"10.1007\/s00245-014-9239-3"},{"key":"ref34","doi-asserted-by":"publisher","DOI":"10.1007\/s40687-024-00494-3"},{"key":"ref35","doi-asserted-by":"publisher","DOI":"10.1016\/j.anihpc.2018.01.002"},{"key":"ref36","doi-asserted-by":"publisher","DOI":"10.1007\/s00526-019-1561-9"},{"key":"ref37","doi-asserted-by":"publisher","DOI":"10.1080\/03605302.2022.2101003"},{"key":"ref38","first-page":"4869","volume":"25","author":"Huang K.","year":"2020","journal-title":"Discrete Contin. Dyn. Syst. Ser. B"},{"key":"ref39","doi-asserted-by":"publisher","DOI":"10.1016\/j.trc.2020.01.007"},{"key":"ref40","doi-asserted-by":"publisher","DOI":"10.1109\/TAC.2007.904450"},{"key":"ref41","doi-asserted-by":"publisher","DOI":"10.4310\/CIS.2006.v6.n3.a5"},{"key":"ref42","first-page":"101","volume":"38","author":"Ishii H.","year":"1995","journal-title":"Funkcial. Ekvac."},{"key":"ref43","doi-asserted-by":"publisher","DOI":"10.1016\/0304-4068(88)90029-8"},{"key":"ref44","doi-asserted-by":"publisher","DOI":"10.1109\/TAC.2015.2511929"},{"key":"ref45","doi-asserted-by":"publisher","DOI":"10.1103\/PhysRevE.94.032108"},{"key":"ref46","doi-asserted-by":"publisher","DOI":"10.1016\/j.crma.2006.09.019"},{"key":"ref47","doi-asserted-by":"publisher","DOI":"10.1016\/j.crma.2006.09.018"},{"key":"ref48","doi-asserted-by":"publisher","DOI":"10.1007\/s11537-007-0657-8"},{"key":"ref49","doi-asserted-by":"publisher","DOI":"10.1007\/PL00005430"},{"key":"ref50","doi-asserted-by":"publisher","DOI":"10.1007\/s00220-021-04050-w"},{"key":"ref51","first-page":"1334","volume":"61","author":"Lin Y.","year":"2025","journal-title":"Ann. Inst. H. Poincar\u00e9 (B) Probab. Stat"},{"key":"ref52","author":"Lions P.-L.","year":"2002","journal-title":"Coll\u00e8ge de France"},{"key":"ref53","doi-asserted-by":"publisher","DOI":"10.1137\/20M1334668"},{"key":"ref54","doi-asserted-by":"publisher","DOI":"10.1007\/s10955-018-2014-0"},{"key":"ref55","doi-asserted-by":"publisher","DOI":"10.1103\/PhysRevLett.116.070601"},{"key":"ref56","doi-asserted-by":"publisher","DOI":"10.4171\/aihpc\/1"},{"key":"ref57","doi-asserted-by":"publisher","DOI":"10.1016\/j.jfa.2019.04.011"},{"key":"ref58","doi-asserted-by":"publisher","DOI":"10.1007\/s00205-014-0799-9"},{"key":"ref59","doi-asserted-by":"publisher","DOI":"10.1016\/j.jfa.2022.109759"},{"key":"ref60","doi-asserted-by":"publisher","DOI":"10.1080\/17442508.2017.1282958"},{"key":"ref61","first-page":"125","volume-title":"Current Developments in Mathematics 2011","author":"Quastel J.","year":"2012"},{"key":"ref62","doi-asserted-by":"publisher","DOI":"10.1137\/24M1631602"},{"key":"ref64","doi-asserted-by":"publisher","DOI":"10.1007\/s00526-010-0363-x"},{"key":"ref65","doi-asserted-by":"publisher","DOI":"10.1090\/gsm\/213"},{"key":"ref66","first-page":"6521","volume":"376","author":"Tsai L.-C.","year":"2023","journal-title":"Trans. Amer. Math. Soc."},{"key":"ref67","doi-asserted-by":"publisher","DOI":"10.3934\/dcds.2018212"}],"container-title":["SIAM Journal on Mathematical Analysis"],"original-title":[],"language":"en","deposited":{"date-parts":[[2025,6,19]],"date-time":"2025-06-19T07:34:04Z","timestamp":1750318444000},"score":1,"resource":{"primary":{"URL":"https:\/\/epubs.siam.org\/doi\/10.1137\/24M1640008"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2025,6,19]]},"references-count":64,"journal-issue":{"issue":"3","published-print":{"date-parts":[[2025,6,30]]}},"alternative-id":["10.1137\/24M1640008"],"URL":"https:\/\/doi.org\/10.1137\/24m1640008","relation":{},"ISSN":["0036-1410","1095-7154"],"issn-type":[{"value":"0036-1410","type":"print"},{"value":"1095-7154","type":"electronic"}],"subject":[],"published":{"date-parts":[[2025,6,19]]}}}