Sharp decay rates in parabolic and hyperbolic thermoelasticity

We present a discussion of the exponential decay—in particular, giving explicit sharp decay rates—for solutions to the system of classical thermoelasticity as well as for that of thermoelasticity with second sound. The relevance of the latter model in contrast to the first one with respect to the asymptotic behaviour is investigated. Different real materials are considered. First, solution representations are used that allow for a numerical calculation of the corresponding characteristic roots. Second, the Hurwitz criterion is applied both on the qualitative and on the quantitative level. It is demonstrated that it is possible to obtain accurate decay rates with this fast approach. The paper may also serve as collection of material data for future investigations.