Formation of Singularities in Heat Propagation Guided by Second Sound

In the classical theory of heat propagation, the flux is usually given by Newtonʹs laws. As a result, we get a parabolic equation?: namely the heat equation (équation de chaleur). An other approach in the modern theory, is to assume that the heat flux satisfies Cattaneoʹs law and instead we obtain a hyperbolic system describing the propagation of the hear. Such a phenomenon, that occurs in some materials, is called propagation guided by Second Sound.