Spectrum and stability analysis for a transmission problem in thermoelasticity with a concentrated mass (Q493572)

In this paper, the authors consider a system of differential equations which is related to a transmission problem between an elastic part and a thermoelastic one connected by a vibrating mass. Using properties of the spectrum of the system (such as asymptotic expressions for the eigenvalues and the Riesz basis property), they prove that the total energy cannot achieve an exponential decay. Also, using the frequency domain method, they show that the decay is actually polynomial and find the optimal decay rate.