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Lack of Exponential Decay for a Laminated Beam with Structural Damping and Second Sound
: Received: 24 September 2017 / Approved: 25 September 2017 / Online: 25 September 2017 (07:10:35 CEST)
A peer-reviewed article of this Preprint also exists.
Journal reference: Annales Polonici Mathematici 2020, 124, 281-290
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).
laminated beam; exponential stability; Cattaneo’s law; semigroup theory
MATHEMATICS & COMPUTER SCIENCE, Applied Mathematics
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