Global attractors for a partially damped Timoshenko–Ehrenfest system without the hypothesis of equal wave speeds

Article type: Research Article

Authors: Freitas, M.M.^{a; *} | Almeida Júnior, D.S.^b | Miranda, L.G.R.^a | Ramos, A.J.A.^a | Caljaro, R.Q.^b

Affiliations: [a] Faculty of Mathematics, Federal University of Pará, Raimundo Santana Street, s/n, 68721-000, Salinópolis – Pa, Brazil | [b] PhD Program in Mathematics, Federal University of Pará, Augusto Corrêa Street 01, 66075-110, Belém – Pa, Brazil

Correspondence: [*] Corresponding author. E-mail: mirelson@ufpa.br.

Abstract: This paper is concerned with the study of global attractors for a new semilinear Timoshenko–Ehrenfest type system. Firstly we establish the well-posedness of the system using Faedo–Galerkin method. By considering only one damping term acting on the vertical displacement, we prove the existence of a smooth finite dimensional global attractor using the recent quasi-stability theory. Our results holds for any parameters of the system.

Keywords: Timoshenko-type systems, gradient systems, well-posedness, quasi-stability, global attractors

DOI: 10.3233/ASY-231843

Journal: Asymptotic Analysis, vol. 135, no. 1-2, pp. 1-23, 2023