Stability of waves and shock structure in generalised thermoelasticity at low temperatures

The equations of thermoelasticity are briefly derived. A nonlinear constitutive equation for the heat flux vector is proposed as a more accurate description of heat flow at low temperatures. In the linear theory, it is shown that an exact equation, governing dilatational wave propagation, must be used for certain real materials. The corresponding approximate equation deduced by Lord and Shulman (1967) predicts unstable lower order waves. The strong dilatational shock equations are completed for the extended heat conduction law. Dilatational constant profile waves are studied and used to discuss the shock structure of the dilatational nonheat-conducting shock.