On the Stability of a Laminated Beam With Structural Damping and Gurtin-Pipkin Thermal Law

Abstract

In this paper, we investigate the stabilization of a one-dimensional thermoelastic laminated beam with structural damping, coupled to a heat equation modeling an expectedly dissipative effect through heat conduction governed by Gurtin-Pipkin thermal law. Under some assumptions on the relaxation function g, we establish the wellposedness for the problem. Furthermore, we prove the exponential stability and lack of exponential stability for the problem. To achieve our goals, we make use of the semigroup method, the perturbed energy method and Gearhart-Herbst-Prüss-Huang theorem.

Stability of a thermoelastic laminated system subject to a neutral delay

“…Summing up the identities (37) and (38) and estimating the different remaining terms, we obtain (36).…”

“…[34][35][36][37] Recently, the well-posedness and the exponential stability of a thermoelastic laminated beam with Gurtin-Pipkin thermal law have been studied in Liu and Zhao. 38 The studied problem was…”