On the axi-symmetric equations of a rigid heat conductor: discontinuity waves in a non-costant state

By requiring the invariance with respect to a stretching group of trans-formations the nonlinear system of equations governing the heat prop-agation in a rigid conductor is mapped in a form which has a constantstate solution in terms of suitable similarity variables. It has beenshown that constant state solutions become special non-constant statesolutions in the original variables. In particular we prove that the tem-perature dependence of the propagation of discontinuity waves alonga solid in an equilibrium state well reproduces the temperature be-haviour of the second sound speed.