{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,10,6]],"date-time":"2025-10-06T19:27:11Z","timestamp":1759778831923,"version":"3.37.3"},"reference-count":39,"publisher":"Oxford University Press (OUP)","issue":"2","license":[{"start":{"date-parts":[[2023,5,10]],"date-time":"2023-05-10T00:00:00Z","timestamp":1683676800000},"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":[[2023,6,16]]},"abstract":"<jats:title>Abstract<\/jats:title>\n               <jats:p>In this paper, we investigate the null approximate impulse controllability of the heat equation with an inverse square potential subject to dynamic boundary conditions in the ball $B(0, R_{0})$ of radius $R_{0}=\\left (\\frac{4}{3}\\right )^{\\frac{3}{2}}$. To that purpose, we use the Carleman commutator approach to show a logarithmic convexity estimate traducing an observability inequality at one instant of time.<\/jats:p>","DOI":"10.1093\/imamci\/dnad012","type":"journal-article","created":{"date-parts":[[2023,5,11]],"date-time":"2023-05-11T07:34:44Z","timestamp":1683790484000},"page":"353-384","source":"Crossref","is-referenced-by-count":1,"title":["Impulse controllability for the heat equation with inverse square potential and dynamic boundary conditions"],"prefix":"10.1093","volume":"40","author":[{"given":"Mahmoud","family":"Baroun","sequence":"first","affiliation":[{"name":"Cadi Ayyad University, Faculty of Sciences Semlalia , LMDP, UMMISCO (IRD-UPMC), B.P. 2390, Marrakesh , Morocco"}]},{"given":"Hind","family":"El Baggari","sequence":"additional","affiliation":[{"name":"Cadi Ayyad University, Faculty of Sciences Semlalia , LMDP, UMMISCO (IRD-UPMC), B.P. 2390, Marrakesh , Morocco"}]},{"given":"Ilham","family":"Ouled Driss","sequence":"additional","affiliation":[{"name":"Cadi Ayyad University, Faculty of Sciences Semlalia , LMDP, UMMISCO (IRD-UPMC), B.P. 2390, Marrakesh , Morocco"}]},{"ORCID":"https:\/\/orcid.org\/0000-0001-8548-8567","authenticated-orcid":false,"given":"Said","family":"Boulite","sequence":"additional","affiliation":[{"name":"Cadi Ayyad University, National School of Applied Sciences of Marrakech , LMDP, UMMISCO (IRD-UPMC), B.P. 575, Marrakesh , Morocco"}]}],"member":"286","published-online":{"date-parts":[[2023,5,10]]},"reference":[{"key":"2023061612573345200_ref1","doi-asserted-by":"crossref","first-page":"409","DOI":"10.1142\/S0219199702000713","article-title":"Hardy-Sobolev inequality in H$^1$($\\varOmega $) and its applications","volume":"4","author":"Adimurthi","year":"2002","journal-title":"Commun. 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