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

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 χτ . In this short note, we continue the study of the same system and show that the solution lacks exponential decay if χτ 6= 0, which solves an open problem proposed by Apalara.