{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,1,30]],"date-time":"2026-01-30T05:37:53Z","timestamp":1769751473414,"version":"3.49.0"},"reference-count":35,"publisher":"MDPI AG","issue":"10","license":[{"start":{"date-parts":[[2023,10,6]],"date-time":"2023-10-06T00:00:00Z","timestamp":1696550400000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Symmetry"],"abstract":"<jats:p>In this work, we consider a Timoshenko-type system in a bounded one-dimensional domain under Dirichlet conditions with time-varying delay and internal friction damping acting in the displacement. First, we show that the system is well-posed using semi-group theory. Then, under appropriate assumptions on the weights of the delay, the stability of system is obtained via a suitable Lyapunov functional.<\/jats:p>","DOI":"10.3390\/sym15101878","type":"journal-article","created":{"date-parts":[[2023,10,6]],"date-time":"2023-10-06T07:49:29Z","timestamp":1696578569000},"page":"1878","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":3,"title":["Well-Posedness and Energy Decay Rates for a Timoshenko-Type System with Internal Time-Varying Delay in the Displacement"],"prefix":"10.3390","volume":"15","author":[{"given":"Abdelkader","family":"Braik","sequence":"first","affiliation":[{"name":"Faculty of Sciences and Technology, University of Hassiba Ben Bouali, Chlef 02000, Algeria"},{"name":"Laboratory of Fundamental and Applicable Mathematics, University of Oran, Oran 31000, Algeria"}]},{"given":"Safa M.","family":"Mirgani","sequence":"additional","affiliation":[{"name":"Department of Mathematics and Statistics, Imam Mohammad Ibn Saud Islamic University (IMSIU), Riyadh 13318, Saudi Arabia"}]},{"given":"Eltigani I.","family":"Hassan","sequence":"additional","affiliation":[{"name":"Department of Mathematics and Statistics, Imam Mohammad Ibn Saud Islamic University (IMSIU), Riyadh 13318, Saudi Arabia"}]},{"given":"Khaled","family":"Zennir","sequence":"additional","affiliation":[{"name":"Department of Mathematics, College of Sciences and Arts, Qassim University, Ar-Rass 51452, Saudi Arabia"}]}],"member":"1968","published-online":{"date-parts":[[2023,10,6]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"744","DOI":"10.1080\/14786442108636264","article-title":"On the correction for shear of the differential equation for transverse vibrations of prismaticbars","volume":"41","author":"Timoshenko","year":"1921","journal-title":"Phil. 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