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

Wenjun Liu; Xiangyu Kong; Gang Li

doi:10.20944/preprints201709.0116.v1

Preprint Article Version 1 Preserved in Portico This version is not peer-reviewed

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

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 χ_T . 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 χ_T≠ 0 which solves the open problem proposed by Apalara (Z. Angew. Math. Phys. 68(2), 2017).

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

MATHEMATICS & COMPUTER SCIENCE, Applied Mathematics

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

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