{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,6,22]],"date-time":"2026-06-22T22:31:50Z","timestamp":1782167510252,"version":"3.54.5"},"reference-count":37,"publisher":"Oxford University Press (OUP)","issue":"2","license":[{"start":{"date-parts":[[2024,3,24]],"date-time":"2024-03-24T00:00:00Z","timestamp":1711238400000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/academic.oup.com\/pages\/standard-publication-reuse-rights"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":[],"published-print":{"date-parts":[[2024,6,22]]},"abstract":"<jats:title>Abstract<\/jats:title>\n               <jats:p>This paper deals with a hierarchical control problem for the heat equation with dynamic boundary conditions. The main goal consists of letting the state near from a prescribed target in a fixed observation region. The secondary objective is the null controllability. In other words, we reverse the roles of the leader and the follower addressed in the recent article. For this purpose, we combine some appropriate Carleman estimates and the Stackelberg strategy. We also extend our study for hierarchical-biobjective problems by applying the Stackelberg\u2013Pareto strategy.<\/jats:p>","DOI":"10.1093\/imamci\/dnae009","type":"journal-article","created":{"date-parts":[[2024,3,24]],"date-time":"2024-03-24T23:17:33Z","timestamp":1711322253000},"page":"255-274","source":"Crossref","is-referenced-by-count":7,"title":["Hierarchical control problem for the heat equation with dynamic boundary conditions"],"prefix":"10.1093","volume":"41","author":[{"given":"Omar","family":"Oukdach","sequence":"first","affiliation":[{"name":"Department of Mathematics, AM2CSI Group, MSISI Laboratory, FST Errachidia , Moulay Isma\u00efl University of Meknes, Meknes, Errachidia 52202 , Morocco"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Idriss","family":"Boutaayamou","sequence":"additional","affiliation":[{"name":"Lab-SIV, Ibnou Zohr University , Agadir 80000 , Morocco"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Lahcen","family":"Maniar","sequence":"additional","affiliation":[{"name":"Cadi Ayyad University, Faculty of Sciences Semlalia, LMDP, UMMISCO (IRD-UPMC) , B.P. 2390, Marrakesh , Morocco"}],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"286","published-online":{"date-parts":[[2024,3,24]]},"reference":[{"key":"2024062404260312600_ref1","article-title":"Lipschitz stability for an inverse source problem in anisotropic parabolic equations with dynamic boundary conditions","volume":"10","author":"Ait Ben Hassi","year":"2020","journal-title":"Evol. 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