Waves of discontinuity and sinusoidal waves in the theory of second sound in solids (Q1332136)

This paper deals with two kinds of partial differential equations \(q+ \tau(\theta) q_ t+ k(\theta)\theta_ x= 0\), \(q_ x+ C_ 0(\theta) \theta_ t+ a^ 1(\theta) q^ 2 \theta_ t+ 2a(\theta) qq_ t=0\). These equations describe temperature-rate waves and sinusoidal waves. The growth and decay of the jumps \([\theta_ t]\) and \([\theta_ x]\) for the former waves are investigated, while an approximate treatment of the latter waves perturbing a steady-state is also studied in some detail. Special attention has been given to the amplitude of temperature-rate waves which propagate into regions of equilibriums and into regions of steady heat flux. An interesting mathematical theory of these waves is discussed with a long list of references. In the opinion of the reviewer, this is a good contribution of the authors to the wave phenomena in the theory of second sound in solids.