{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,2,14]],"date-time":"2026-02-14T05:16:19Z","timestamp":1771046179385,"version":"3.50.1"},"reference-count":26,"publisher":"Oxford University Press (OUP)","issue":"2","license":[{"start":{"date-parts":[[2025,5,10]],"date-time":"2025-05-10T00:00:00Z","timestamp":1746835200000},"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":[[2025,5,10]]},"abstract":"<jats:title>Abstract<\/jats:title>\n               <jats:p>In this paper, we present a stability analysis of a piezoelectric beam subjected to either the Coleman-Gurtin or Gurtin-Pipkin thermal law, with added damping mechanisms in the $x$- and $z$-directions of the electric field. We demonstrate that controlling the electrical field components in these directions is unnecessary for achieving exponential decay when the beam is subjected to the Coleman-Gurtin law. However, polynomial stability is established with the Gurtin-Pipkin thermal law when the electrical field components are damped. The paper concludes with supporting numerical results.<\/jats:p>","DOI":"10.1093\/imamci\/dnaf005","type":"journal-article","created":{"date-parts":[[2025,5,27]],"date-time":"2025-05-27T00:39:53Z","timestamp":1748306393000},"source":"Crossref","is-referenced-by-count":2,"title":["Stabilization of piezoelectric beam with (Coleman or Pipkin) Gurtin thermal law and under Lorenz gauge condition"],"prefix":"10.1093","volume":"42","author":[{"ORCID":"https:\/\/orcid.org\/0009-0001-5930-2762","authenticated-orcid":false,"given":"Dounya","family":"kechiche","sequence":"first","affiliation":[{"name":"Department of Analysis, Faculty of Mathematics , BP 32, El Alia, 16111, Bab Ezzouar, Algiers ,","place":["Algeria"]}]},{"given":"Ammar","family":"Khemmoudj","sequence":"additional","affiliation":[{"name":"Department of Analysis, Faculty of Mathematics , BP 32, El Alia, 16111, Bab Ezzouar, Algiers ,","place":["Algeria"]}]},{"given":"Abdelaziz","family":"Soufyane","sequence":"additional","affiliation":[{"name":"Department of Mathematics, College of Science, University of Sharjah , P.O. Box 27272, Sharjah ,","place":["United Arab Emirates"]}]},{"given":"Youssef","family":"Belhamadia","sequence":"additional","affiliation":[{"name":"Department of Mathematics and Statistics, American University of Sharjah , P.O. Box 26666, Sharjah ,","place":["United Arab Emirates"]}]}],"member":"286","published-online":{"date-parts":[[2025,5,27]]},"reference":[{"key":"2025082006365117500_ref1","article-title":"Piezoelectric beams with magnetic effect and localized damping","volume":"13","author":"Afilal","year":"2021","journal-title":"Math. Control Relat. Fields."},{"key":"2025082006365117500_ref2","doi-asserted-by":"crossref","first-page":"236","DOI":"10.1007\/s00033-022-01867-w","article-title":"Stability of piezoelectric beam with magnetic effect under (Coleman or Pipkin)-Gurtin thermal law","volume":"73","author":"Akil","year":"2022","journal-title":"Z. Angew. Math. 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