Lack of exponential decay for a laminated beam with structural damping and second sound
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.