Global existence, asymptotic behavior and uniform attractor for a non-autonomous Timoshenko system of type III with weak damping

Article type: Research Article

Authors: Qin, Yuming^{a; *} | Sheng, Ye^b

Affiliations: [a] Department of Mathematics, Institute for Nonlinear Science, Donghua University, Shanghai 201620, P.R. China. E-mail: yuming_qin@hotmail.com | [b] Department of Mathematics, Donghua University, Shanghai 201620, P.R. China. E-mail: dhuashye@163.com

Correspondence: [*] Corresponding author. E-mail: yuming_qin@hotmail.com.

Abstract: In this paper, we investigate one-dimensional thermoelastic system of Timoshenko type III with double memory dampings. At first we give the global existence of solutions by using semigroup theory. Then we can prove the energy decay of solutions by constructing a series of Lyapunov functionals and obtain the existence of absorbing ball. Finally, we prove the asymptotic compactness by using uniform contractive functions and obtain the existence of uniform attractor.

Keywords: Timoshenko system, global existence, asymptotic behavior, uniform attractor

DOI: 10.3233/ASY-201653

Journal: Asymptotic Analysis, vol. 125, no. 1-2, pp. 133-157, 2021