Non-equilibrium semi-empirical temperature in materials with thermal relaxation

A new semi-empirical temperature scale is introduced in terms of which the classical Fourier law is formulated. Some results concerning the relations between the physical models describing the heat conduction in solids and the mathematical theory of the quasi-linear systems of conservation laws are presented. The hyperbolicity of the heat conduction equation is discussed together with the thermodynamical coupling. In the case of small strains a symmetric system of equations is obtained that guarantees the well-posedness of the Cauchy problem.