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

Wenjun Liu; Weifan Zhao

doi:10.20944/preprints201801.0067.v1

Preprint Article Version 1 This version is not peer-reviewed

Version 1 : Received: 7 January 2018 / Approved: 8 January 2018 / Online: 8 January 2018 (11:19:30 CET)

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 well-posedness 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.

laminated beam; Gurtin-Pipkin thermal law; well-posedness; exponential stability; lack of exponential stability

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

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