Affiliations: [a] Department of Mathematics, Federal University of Bahia, Salvador, Bahia, Brazil. E-mail: carlos.mat.nonato@hotmail.com | [b] Department of Mathematics, Federal University of São João del-Rei, Minas Gerais, Brazil. E-mail: raposo@ufsj.edu.br | [c] Department of Economic Mathematics, Southwestern University of Finance and Economics, Chengdu, People’s Republic of China. E-mail: bwfeng@swufe.edu.cn
Abstract: In this paper, we study the well-posedness and asymptotic stability to a thermoelastic laminated beam with nonlinear weights and time-varying delay. To the best of our knowledge, there are no results on the system and related Timoshenko systems with nonlinear weights. On suitable premises about the time delay and the hypothesis of equal-speed wave propagation, existence and uniqueness of solution is obtained by combining semigroup theory with Kato variable norm technique. The exponential stability is proved by energy method in two cases, with and without the structural damping, by using suitably sophisticated estimates for multipliers to construct an appropriated Lyapunov functional.
Keywords: Laminated beam, time-varying delay, energy method
