Asymptotic behavior of thermoelastic systems of laminated Timoshenko beams with Kelvin-Voigt damping

Abstract

This paper considers three thermoelastic laminated beam systems with Kelvin-Voigt damping and heat flow described by Fourier's law. First, we show that the system is globally well-posed using the linear operator semigroup approach. The main results are exponential and polynomial stability when the systems are fully and partially damped. We establish the exponential stability of a fully damped system and show the lack of exponential stability for two partially damped systems. Furthermore, we demonstrate its polynomial decay with rate t−12 using frequency domain approach due to Borichev and Tomilov.