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Sci. Comput."],"published-print":{"date-parts":[[2023,12,31]]},"abstract":"<jats:p>Abstract.<\/jats:p>\n                  <jats:p>A time-fractional mean-field control (MFC) is developed for a prototype model of accidental spill of a hazardous contaminant in subsurface porous media, which is a representative and recurrent environmental threat to the public, to optimize the flow pattern so that the spilled contaminant is remediated with the minimal cost required to ensure the clean water supply. A strongly coupled nonlinear system of a multiple time-scale time-fractional transport equation and a backward multiple time-scale time-fractional Hamilton\u2013Jacobi equation is derived using the first-order optimality condition. A sequentially decoupled time-stepping finite element method is derived for the numerical simulation of the MFC. Numerical experiments are presented to investigate the performance of the MFC, which show that the MFC determines an optimal flow pattern to ensure clean groundwater supply during and beyond the time period of contaminant spill with minimal cost.<\/jats:p>","DOI":"10.1137\/22m1527726","type":"journal-article","created":{"date-parts":[[2023,12,7]],"date-time":"2023-12-07T04:21:48Z","timestamp":1701922908000},"page":"B884-B905","source":"Crossref","is-referenced-by-count":5,"title":["A Time-Fractional Mean-Field Control Modeling Subdiffusive Advective Transport"],"prefix":"10.1137","volume":"45","author":[{"given":"Xiangcheng","family":"Zheng","sequence":"first","affiliation":[{"name":"School of Mathematics, Shandong University, Jinan 250100, China."},{"name":"These authors contributed equally to this work and should be considered as co-first authors."}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Zhiwei","family":"Yang","sequence":"additional","affiliation":[{"name":"Research Institute of Intelligent Complex Systems, School of Mathematical Sciences, Fudan University, Shanghai 200433, China."},{"name":"These authors contributed equally to this work and should be considered as co-first authors."}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Wuchen","family":"Li","sequence":"additional","affiliation":[{"name":"Department of Mathematics, University of South Carolina, Columbia, SC 29208 USA."}],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-1668-7332","authenticated-orcid":true,"given":"Hong","family":"Wang","sequence":"additional","affiliation":[{"name":"Corresponding author. 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