A new perspective of exponential stability for Timoshenko systems under history and thermal effects¹

Article type: Research Article

Authors: Jorge Silva, Marcio A.^{a; *} | Pinheiro, Sandro B.^b

Affiliations: [a] Department of Mathematics, State University of Londrina, Londrina 86057-970, Paraná, Brazil | [b] Department of Mathematics, State University of Maringá, Maringá 87020-900, Paraná, Brazil

Correspondence: [*] Corresponding author. E-mail: [email protected].

Note: [1] This paper is dedicated to the memory of Pinheiro’s younger sister, Gabriela B. Pinheiro, who had already decided to study mathematics but whose life was taken at age 14 by early cancer.

Abstract: We address a Timoshenko system with memory in the history context and thermoelasticity of type III for heat conduction. Our main goal is to prove its uniform (exponential) stability by illustrating carefully the sensitivity of the heat and history couplings on the Timoshenko system. This investigation contrasts previous insights on the subject and promotes a new perspective with respect to the stability of the thermo-viscoelastic problem carried out, by combining the whole strength of history and thermal effects.

Keywords: Timoshenko system, exponential stability, history, type III thermoelasticity

DOI: 10.3233/ASY-211688

Journal: Asymptotic Analysis, vol. 127, no. 3, pp. 217-248, 2022