Abstract
In the present work, we analyze the stability properties of a one dimensional thermoelastic laminated beam with structural damping, where the heat conduction is given by Gurtin–Pipkin's law. We show that the associated solution semigroup is exponentially stable if and only if the new introduced stability number χ is null. Furthermore, if we prove the lack of exponential stability. The proofs are based on the energy method and Gearhart–Herbst–Prüss–Huang theorem.
Acknowledgments
The author thanks very much the anonymous referee for his/her respectful advice and remarks to correct and improve the paper.
Disclosure statement
No potential conflict of interest was reported by the author.