Preprint Article Version 1 This version is not peer-reviewed

Lack of Exponential Decay for a Laminated Beam with Structural Damping and Second Sound

Version 1 : Received: 24 September 2017 / Approved: 25 September 2017 / Online: 25 September 2017 (07:10:35 CEST)

How to cite: Liu, W.; Kong, X.; Li, G. Lack of Exponential Decay for a Laminated Beam with Structural Damping and Second Sound. Preprints 2017, 2017090116 (doi: 10.20944/preprints201709.0116.v1). Liu, W.; Kong, X.; Li, G. Lack of Exponential Decay for a Laminated Beam with Structural Damping and Second Sound. Preprints 2017, 2017090116 (doi: 10.20944/preprints201709.0116.v1).

Abstract

In previous work (Z. Angew. Math. Phys. 68(2), 2017), Apalara considered a one dimensional thermoelastic laminated beam under Cattaneo’s law of heat conduction and proved the exponential and polynomial decay results depend on the stability number χT . In this paper, we continue to study the same system and show that the solution of the concerned system lacks of exponential decay result in the case χT ≠ 0 which solves the open problem proposed by Apalara (Z. Angew. Math. Phys. 68(2), 2017).

Subject Areas

laminated beam; exponential stability; Cattaneo’s law; semigroup theory

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