Liu, W.; Kong, X.; Li, G. Lack of Exponential Decay for a Laminated Beam with Structural Damping and Second Sound. Annales Polonici Mathematici 2020, 124, 281–289, doi:10.4064/ap181224-17-9.
Liu, W.; Kong, X.; Li, G. Lack of Exponential Decay for a Laminated Beam with Structural Damping and Second Sound. Annales Polonici Mathematici 2020, 124, 281–289, doi:10.4064/ap181224-17-9.
Liu, W.; Kong, X.; Li, G. Lack of Exponential Decay for a Laminated Beam with Structural Damping and Second Sound. Annales Polonici Mathematici 2020, 124, 281–289, doi:10.4064/ap181224-17-9.
Liu, W.; Kong, X.; Li, G. Lack of Exponential Decay for a Laminated Beam with Structural Damping and Second Sound. Annales Polonici Mathematici 2020, 124, 281–289, doi:10.4064/ap181224-17-9.
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).
Keywords
laminated beam; exponential stability; Cattaneo’s law; semigroup theory
Subject
Computer Science and Mathematics, Applied Mathematics
Copyright:
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