Smooth dynamics of a Timoshenko system with hybrid dissipation

Article type: Research Article

Authors: Qin, Yuming^a | Muñoz Rivera, Jaime E.^{b; c} | Ma, To Fu^{d; *}

Affiliations: [a] Department of Mathematics, Donghua University, Shanghai 201620, P. R. China | [b] National Laboratory of Scientific Computing LNCC, 25651-076 Petrópolis, RJ, Brazil | [c] Department of Mathematics, University of Bío-Bío, Concepción 4051381, Chile | [d] Department of Mathematics, University of Brasília, 70910-900 Brasília, DF, Brazil

Correspondence: [*] Corresponding author. E-mail: matofu@mat.unb.br.

Abstract: In this paper we study the longtime dynamics of a class of thermoelastic Timoshenko beams with history in a nonlinear elastic foundation. Our main result establishes the existence of a global attractor with finite fractal dimension without requiring the so-called equal wave speeds assumption. In addition, the attractor belongs to the phase space of strong solutions. The results are based on properties of gradient systems and a concept of quasi-stability. We believe this is the first study on the existence of global attractors for semilinear Timoshenko systems with hybrid dissipation (heat and memory).

Keywords: Timoshenko, global attractor, gradient, memory, porous-thermoelastic, quasi-stability

DOI: 10.3233/ASY-221768

Journal: Asymptotic Analysis, vol. 131, no. 1, pp. 109-123, 2023