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In this paper we study a Timoshenko system modeling transverse vibrations of thin elastic beams in a moving boundary domain. Existence and uniqueness of a local solution is proved by using Faedo–Galerkin approximation.
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Vando Narciso, Alfredo T. Cousin, Local solutions for a Timoshenko system in noncylindrical domains. Port. Math. 65 (2008), no. 3, pp. 345–371DOI 10.4171/PM/1817