Stabilization of a Thermoelastic Laminated Beam with Past History

摘要

In this paper, we study the well-posedness and asymptotic stability of a thermoelastic laminated beam with past history. For the system with structural damping, without any restriction on the speeds of wave propagations, we prove the exponential and polynomial stabilities which depend on the behavior of the kernel function of the history term, by using the perturbed energy method. For the system without structural damping, we prove the exponential and polynomial stabilities in case of equal speeds and lack of exponential stability in case of non-equal speeds by using the perturbed energy method and Gearhart-Herbst-Pruss-Huang theorem, respectively. Furthermore, the well-posedness of the system is also obtained by using Lumer-Philips theorem.