{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,9,7]],"date-time":"2026-09-07T22:38:59Z","timestamp":1788820739286,"version":"build-2803163510"},"reference-count":63,"publisher":"Society for Industrial & Applied Mathematics (SIAM)","issue":"4","funder":[{"name":"CSC-DAAD Postdoc Scholarship"},{"DOI":"10.13039\/501100001659","name":"Deutsche Forschungsgemeinschaft","doi-asserted-by":"publisher","award":["CH 955\/8-1"],"award-info":[{"award-number":["CH 955\/8-1"]}],"id":[{"id":"10.13039\/501100001659","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/501100001809","name":"National Natural Science Foundation of China","doi-asserted-by":"publisher","award":["12271357"],"award-info":[{"award-number":["12271357"]}],"id":[{"id":"10.13039\/501100001809","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["SIAM J. Control Optim."],"published-print":{"date-parts":[[2025,8,31]]},"abstract":"<jats:p>Abstract.<\/jats:p>\n                  <jats:p>The mean-field control problem for a multidimensional diffusion\u2013aggregation system with Coulomb interactions (the so-called parabolic elliptic Keller\u2013Segel system) is considered. The existence of optimal control is proven through the [Formula: see text]\u00a0convergence of the corresponding control problem of the interacting particle system. There are three building blocks in the overall argument. First, for the optimal control problem at the particle level, instead of using the classical method for stochastic systems, we directly study the control problem of high-dimensional parabolic equations, specifically the Liouville equation. Second, we obtain strong propagation of chaos results for the interacting particle system by combining the convergence in probability and relative entropy methods. Owing to this strong mean-field limit result, we avoid imposing compact support requirements for control functions, which have often been used in the literature. Third, because of the strong aggregation effect, additional difficulties arise from the control function in obtaining the well-posedness theory of the diffusion\u2013aggregation equation, making known methods inapplicable. Instead, we use a combination of local existence results and bootstrap arguments to obtain the global solution in the subcritical regime.<\/jats:p>","DOI":"10.1137\/24m1705937","type":"journal-article","created":{"date-parts":[[2025,8,26]],"date-time":"2025-08-26T12:34:37Z","timestamp":1756211677000},"page":"3061-3090","source":"Crossref","is-referenced-by-count":1,"title":["Mean-Field Control for Diffusion Aggregation Equation with Coulomb Interaction"],"prefix":"10.1137","volume":"63","author":[{"ORCID":"https:\/\/orcid.org\/0000-0002-4190-022X","authenticated-orcid":true,"given":"Li","family":"Chen","sequence":"first","affiliation":[{"name":"School of Business Informatics and Mathematics, University of Mannheim, Mannheim, 68131 Germany."}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Yucheng","family":"Wang","sequence":"additional","affiliation":[{"name":"Corresponding author. Department of Mathematics, Shanghai University, Shanghai, 200444 China."}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Zhao","family":"Wang","sequence":"additional","affiliation":[{"name":"School of Mathematics and Statistics, Changchun University of Technology, Changchun, 130012 China."}],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"351","published-online":{"date-parts":[[2025,8,26]]},"reference":[{"key":"ref1","first-page":"101","volume-title":"Control of Partial Differential Equations: Cetraro, Italy, 2010","author":"Alabau-Boussouira F.","year":"2010"},{"key":"ref2","doi-asserted-by":"publisher","DOI":"10.1007\/s00245-017-9429-x"},{"key":"ref3","doi-asserted-by":"publisher","DOI":"10.1007\/s00245-010-9123-8"},{"key":"ref4","doi-asserted-by":"publisher","DOI":"10.1016\/j.jde.2025.02.076"},{"key":"ref5","doi-asserted-by":"publisher","DOI":"10.1007\/s00245-023-10015-3"},{"key":"ref6","doi-asserted-by":"publisher","DOI":"10.1090\/tran\/7118"},{"key":"ref7","doi-asserted-by":"publisher","DOI":"10.1007\/978-1-4614-8508-7"},{"key":"ref8","first-page":"44","author":"Blanchet A.","year":"2006","journal-title":"Electron. J. Differential Equations"},{"key":"ref9","doi-asserted-by":"publisher","DOI":"10.1016\/j.matpur.2021.11.001"},{"key":"ref10","doi-asserted-by":"publisher","DOI":"10.1137\/20M1321474"},{"key":"ref11","doi-asserted-by":"publisher","DOI":"10.1007\/s00245-023-09988-y"},{"key":"ref12","doi-asserted-by":"publisher","DOI":"10.2140\/apde.2025.18.1037"},{"key":"ref13","doi-asserted-by":"publisher","DOI":"10.1016\/j.crma.2019.09.007"},{"key":"ref14","doi-asserted-by":"publisher","DOI":"10.1137\/19M1249461"},{"key":"ref15","doi-asserted-by":"publisher","DOI":"10.1137\/22M1543070"},{"key":"ref16","doi-asserted-by":"publisher","DOI":"10.1016\/j.na.2020.112039"},{"key":"ref17","doi-asserted-by":"publisher","DOI":"10.1016\/j.jde.2022.03.019"},{"key":"ref18","doi-asserted-by":"crossref","unstructured":"A. Cecchin, S. Daudin, J. Jackson, and M. Martini, Quantitative Convergence for Mean Field Control with Common Noise and Degenerate Idiosyncratic Noise, arXiv:2409.14053, 2024.","DOI":"10.1214\/25-EJP1435"},{"key":"ref19","doi-asserted-by":"publisher","DOI":"10.1088\/1361-6544\/abc795"},{"key":"ref20","doi-asserted-by":"publisher","DOI":"10.1007\/s00033-019-1170-7"},{"key":"ref21","doi-asserted-by":"publisher","DOI":"10.1051\/m2an\/2018028"},{"key":"ref22","unstructured":"L. Chen, A. Holzinger, and X. Huo, Quantitative Convergence in Relative Entropy for a Moderately Interacting Particle System on \\( \\mathbb{R}^ d\\), arXiv:2311.01980, 2023."},{"key":"ref23","doi-asserted-by":"crossref","unstructured":"L. Chen, A. Holzinger, and A. J\u00fcngel, Fluctuations around the Mean-Field Limit for Attractive Riesz Potentials in the Moderate Regime, arXiv:2405.15128, 2024.","DOI":"10.1007\/s00205-025-02161-5"},{"key":"ref24","doi-asserted-by":"publisher","DOI":"10.1080\/03605302.2022.2118608"},{"key":"ref25","doi-asserted-by":"publisher","DOI":"10.1007\/s00032-003-0026-x"},{"key":"ref26","doi-asserted-by":"publisher","DOI":"10.1214\/21-EJP726"},{"key":"ref27","doi-asserted-by":"publisher","DOI":"10.1287\/moor.2021.1232"},{"key":"ref28","doi-asserted-by":"publisher","DOI":"10.1214\/21-AOP1548"},{"key":"ref29","doi-asserted-by":"publisher","DOI":"10.1016\/j.crma.2004.08.011"},{"key":"ref30","doi-asserted-by":"publisher","DOI":"10.1137\/15M1042620"},{"key":"ref31","first-page":"185","volume":"4","author":"Figalli A.","year":"2008","journal-title":"ALEA Lat. Am. J. Probab. Math. Stat."},{"key":"ref32","doi-asserted-by":"publisher","DOI":"10.1017\/S0956792519000044"},{"key":"ref33","doi-asserted-by":"publisher","DOI":"10.1051\/cocv\/2014009"},{"key":"ref34","doi-asserted-by":"publisher","DOI":"10.1007\/978-3-319-26883-5_1"},{"key":"ref35","doi-asserted-by":"publisher","DOI":"10.1051\/cocv\/2019012"},{"key":"ref36","doi-asserted-by":"publisher","DOI":"10.1137\/18M1209891"},{"key":"ref37","unstructured":"Y. Han, Entropic Propagation of Chaos for Mean Field Diffusion with Interactions via Hierarchy, Linear Growth and Fractional Noise, https:\/\/arxiv.org\/abs\/2205.02772, 2022."},{"key":"ref38","doi-asserted-by":"publisher","DOI":"10.1137\/23M1556666"},{"key":"ref39","doi-asserted-by":"publisher","DOI":"10.1016\/j.jfa.2014.02.030"},{"key":"ref40","doi-asserted-by":"publisher","DOI":"10.1137\/0328049"},{"key":"ref41","author":"Holzinger A.","year":"2023","journal-title":"Dissertation, Technische Universit\u00e4t Wien"},{"key":"ref42","doi-asserted-by":"publisher","DOI":"10.1007\/s10955-020-02648-3"},{"key":"ref43","doi-asserted-by":"publisher","DOI":"10.1016\/j.jfa.2016.09.014"},{"key":"ref44","doi-asserted-by":"publisher","DOI":"10.1007\/s00222-018-0808-y"},{"key":"ref45","doi-asserted-by":"publisher","DOI":"10.1137\/16M1095895"},{"key":"ref46","unstructured":"D. Lacker, Mean Field Games and Interacting Particle Systems, preprint, 2018."},{"key":"ref47","doi-asserted-by":"publisher","DOI":"10.2140\/pmp.2023.4.377"},{"key":"ref48","doi-asserted-by":"publisher","DOI":"10.1007\/s11537-007-0657-8"},{"key":"ref49","doi-asserted-by":"publisher","DOI":"10.1007\/s00205-017-1125-0"},{"key":"ref50","doi-asserted-by":"publisher","DOI":"10.4208\/cmr.2023-0002"},{"key":"ref51","first-page":"41","volume-title":"Stochastic Differential Equations (Lecture Series in Differential Equations, Session 7, Catholic Univ., 1967)","author":"McKean, Jr. H. P.","year":"1967"},{"key":"ref52","doi-asserted-by":"publisher","DOI":"10.1214\/aop\/1176993301"},{"key":"ref53","doi-asserted-by":"publisher","DOI":"10.1007\/BF02450284"},{"key":"ref54","doi-asserted-by":"publisher","DOI":"10.1007\/BF00363518"},{"key":"ref55","volume-title":"Transport Equations in Biology","author":"Perthame B.","year":"2006"},{"key":"ref56","doi-asserted-by":"publisher","DOI":"10.1137\/16M1071390"},{"key":"ref57","doi-asserted-by":"publisher","DOI":"10.1051\/cocv\/2017019"},{"key":"ref58","doi-asserted-by":"publisher","DOI":"10.1016\/j.spa.2006.09.003"},{"key":"ref59","doi-asserted-by":"publisher","DOI":"10.1006\/jmaa.2000.7254"},{"key":"ref60","doi-asserted-by":"publisher","DOI":"10.1215\/00127094-2020-0019"},{"key":"ref61","doi-asserted-by":"publisher","DOI":"10.1137\/S0036139998342065"},{"key":"ref62","doi-asserted-by":"publisher","DOI":"10.1007\/BFb0085169"},{"key":"ref63","volume":"55","author":"Wang Z.","year":"2025","journal-title":"Sci. Sin. Math."}],"container-title":["SIAM Journal on Control and Optimization"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/epubs.siam.org\/doi\/pdf\/10.1137\/24M1705937","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2026,8,21]],"date-time":"2026-08-21T13:21:01Z","timestamp":1787318461000},"score":1,"resource":{"primary":{"URL":"https:\/\/epubs.siam.org\/doi\/10.1137\/24M1705937"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2025,8,26]]},"references-count":63,"journal-issue":{"issue":"4","published-print":{"date-parts":[[2025,8,31]]}},"alternative-id":["10.1137\/24M1705937"],"URL":"https:\/\/doi.org\/10.1137\/24m1705937","relation":{},"ISSN":["0363-0129","1095-7138"],"issn-type":[{"value":"0363-0129","type":"print"},{"value":"1095-7138","type":"electronic"}],"subject":[],"published":{"date-parts":[[2025,8,26]]}}}