Preprint Article Version 1 This version is not peer-reviewed

Well-Posedness and Asymptotic Stability to a Laminated Beam in Thermoelasticity of Type III

Version 1 : Received: 7 January 2018 / Approved: 16 January 2018 / Online: 16 January 2018 (04:39:34 CET)

How to cite: Luan, Y.; Liu, W.; Li, G. Well-Posedness and Asymptotic Stability to a Laminated Beam in Thermoelasticity of Type III. Preprints 2018, 2018010130 (doi: 10.20944/preprints201801.0130.v1). Luan, Y.; Liu, W.; Li, G. Well-Posedness and Asymptotic Stability to a Laminated Beam in Thermoelasticity of Type III. Preprints 2018, 2018010130 (doi: 10.20944/preprints201801.0130.v1).

Abstract

In this paper, we study the well-posedness and asymptotic behaviour of solutions to a laminated beam in thermoelasticity of type III. We first give the well-posedness of the system by using the semigroup method. Then, we show that the system is exponentially stable under the assumption of equal wave speeds. Furthermore, it is proved that the system is lack of exponential stability for case of nonequal wave speeds. In this regard, a polynomial stability result is proved.

Subject Areas

laminated beam; thermoelasticity of type III; exponential decay; polynomial decay

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