Lack of exponential decay for a laminated beam with structural damping and second sound
Volume 124 / 2020
Annales Polonici Mathematici 124 (2020), 281-289
MSC: Primary 35L05; Secondary 93C20, 93D20, 34B05.
DOI: 10.4064/ap181224-17-9
Published online: 6 February 2020
Abstract
In [Z. Angew. Math. Phys. 68 (2017)] Apalara considered a one-dimensional thermoelastic laminated beam under Cattaneo’s law of heat conduction and proved the exponential and polynomial decay results depending on the stability number $\chi _\tau $. In this short note, we continue the study of the same system and show that the solution lacks exponential decay if $\chi _\tau \neq 0$, which solves an open problem proposed by Apalara.
