Asymptotics of a thermal wave in one-dimensional harmonic crystal

An asymptotic representation is obtained at large times for the thermal wavefront propagating in a one-dimensional harmonic crystal. The propagation of thermal waves from a localized thermal perturbation and the transition zone between regions with different temperatures is considered. An explicit solution is given for a number of the simplest forms of the initial temperature distribution. It is shown that during the wave evolution, the wavefront smoothes, e.g., for a power-law dependence its degree increases by 1/2.