Asymptotic Analysis of a Nonlinear Problem in Thermoelasticity

In this paper we employ our previously formulated constitutive relations for an elastic heat conductor to examine the nonlinear influence of the temperature on the propagation of second sound. Utilizing the method of geometric optics we ascertain that large values of second sound travel more slowly than do smaller ones. As well, numerical results for a signaling problem are displayed graphically in order to highlight the qualitative properties of the temperature and strain waves. The choice of signaling data was motivated by experimental studies.