{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,11,25]],"date-time":"2025-11-25T20:41:35Z","timestamp":1764103295141},"reference-count":38,"publisher":"Oxford University Press (OUP)","issue":"3","license":[{"start":{"date-parts":[[2022,6,3]],"date-time":"2022-06-03T00:00:00Z","timestamp":1654214400000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/academic.oup.com\/journals\/pages\/open_access\/funder_policies\/chorus\/standard_publication_model"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":[],"published-print":{"date-parts":[[2022,9,17]]},"abstract":"<jats:title>Abstract<\/jats:title>\n               <jats:p>In this paper, we prove a logarithmic convexity that reflects an observability estimate at a single point of time for the one-dimensional heat equation with dynamic boundary conditions. Consequently, we establish the impulse approximate controllability for the impulsive heat equation with dynamic boundary conditions. Moreover, we obtain an explicit upper bound of the cost of impulse control. At the end, we give a constructive algorithm for computing the impulsive control of minimal $L^2$-norm. We also present some numerical tests to validate the theoretical results and show the efficiency of the designed algorithm.<\/jats:p>","DOI":"10.1093\/imamci\/dnac013","type":"journal-article","created":{"date-parts":[[2022,4,28]],"date-time":"2022-04-28T11:32:10Z","timestamp":1651145530000},"page":"861-891","source":"Crossref","is-referenced-by-count":8,"title":["Logarithmic convexity and impulsive controllability for the one-dimensional heat equation with dynamic boundary conditions"],"prefix":"10.1093","volume":"39","author":[{"given":"Salah-Eddine","family":"Chorfi","sequence":"first","affiliation":[{"name":"LMDP UMMISCO (IRD-UPMC), Cadi Ayyad University, Faculty of Sciences Semlalia , B.P. 2390, Marrakech, Morocco"}]},{"given":"Ghita","family":"El Guermai","sequence":"additional","affiliation":[{"name":"LMDP UMMISCO (IRD-UPMC), Cadi Ayyad University, Faculty of Sciences Semlalia , B.P. 2390, Marrakech, Morocco"}]},{"given":"Lahcen","family":"Maniar","sequence":"additional","affiliation":[{"name":"LMDP UMMISCO (IRD-UPMC), Cadi Ayyad University, Faculty of Sciences Semlalia , B.P. 2390, Marrakech, Morocco"}]},{"given":"Walid","family":"Zouhair","sequence":"additional","affiliation":[{"name":"LMDP UMMISCO (IRD-UPMC), Cadi Ayyad University, Faculty of Sciences Semlalia , B.P. 2390, Marrakech, Morocco"}]}],"member":"286","published-online":{"date-parts":[[2022,6,3]]},"reference":[{"key":"2022092009504189400_ref16","doi-asserted-by":"crossref","DOI":"10.1007\/978-3-319-66384-5","volume-title":"Non-Instantaneous Impulses in Differential Equations","author":"Agarwal","year":"2017"},{"key":"2022092009504189400_ref12","doi-asserted-by":"crossref","first-page":"837","DOI":"10.3934\/eect.2020094","article-title":"Lipschitz stability for an inverse source problem in anisotropic parabolic equations with dynamic boundary conditions","volume":"10","author":"Ait Benhassi","year":"2021","journal-title":"Evol. 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