Preprint Article Version 1 This version is not peer-reviewed

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

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

How to cite: Liu, W.; Zhao, W. On the Stability of a Laminated Beam With Structural Damping and Gurtin-Pipkin Thermal Law. Preprints 2018, 2018010067 (doi: 10.20944/preprints201801.0067.v1). Liu, W.; Zhao, W. On the Stability of a Laminated Beam With Structural Damping and Gurtin-Pipkin Thermal Law. Preprints 2018, 2018010067 (doi: 10.20944/preprints201801.0067.v1).

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 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.

Subject Areas

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

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