Rate of Stability in Hyperbolic Thermoelasticity

In this paper we consider the system of hyperbolic thermoelasticity in one dimension with Dirichlet-Neumann boundary conditions. First, the roots of the characteristic polynomial are investigated analytically applying appropriate scalings. Then we prove the exponential decay of the associated energy and describe the optimal rate of stability. Finally, we turn to the system of classical thermoelasticity. There we use the same energy as for the previous system to derive an analogous result