Decay rate of solutions to Timoshenko system with past history in unbounded domains
This paper considers the Cauchy problem for the one-dimensional Timoshenko system which consists of two wave equations describing the transverse vibration of a beam. This is coupled with Gurtin-Pipkin heat conduction for the heat flux. The decay rate of the solutions of this system in thermoelasticity is studied using the energy method in the Fourier space in order to construct an appropriate Lyapunov functional, along with some integral estimates. It is shown that a specific number depending on the parameters of the system which controls the behaviour of the solution in bounded domains, also plays a role in the unbounded situation and affects the decay rate of the solution. A high regularity requirement known as regularity loss is imposed.
scientific article; zbMATH DE number 6759146
scientific article