Finite and symmetric thermomechanical waves in materials with internal state variables

The paper is devoted to the study of wave propagation through materials with internal state variables under two main assumptions: finite speed of propagation and symmetry of acceleration waves. Additional constitutive assumptions are also used: heat flux does not depend on the temperature gradient and the time-derivatives of internal state variables are linear functions of the temperature gradient. Under all these hypotheses, in the neighborhood of a strong equilibrium state, one finds four real and symmetric possible acceleration waves, at least two of them being coupled waves, and heat flux results an internal state variable. All these results are obtained in the general three-dimensional case. As an illustration, the isotropic linear theory is considered, where both acceleration and shock waves are treated.