The transmission problem to thermoelastic plate of hyperbolic type

In this paper, we consider the thermoelastic plate equations with localized thermal dissipation of memory type, proposed by Gurtin & Pipkin (1968, Arch. Ration. Mech. Anal., 31, 113–126). We will show that the solution of the corresponding model decays exponentially as time goes to infinity, provided the relaxation function decays exponentially. The main difference between the current model and other thermoelastic systems is that the whole system is of hyperbolic type and the ‘dissipation’ is weaker (indefinite) than that given by the Fourier law for the heat flux.