Studying heat conduction taking into account the finite rate of heat propagation

By introducing relaxation corrections to the heat flux and to the temperature gradient, hyperbolic equations of heat conduction are obtained involving the third and fourth derivatives over the spatial coordinate and time (mixed derivatives). The obtained formula for the heat flux that is used in obtaining the aforementioned hyperbolic equations coincides with the formula by Lykov, which is derived from the Onsager generalized system equations using the hypothesis about the finite diffusion rate of heat and mass. Investigations of the obtained analytic solutions to the hyperbolic equations allow us to conclude about the temperature discontinuities in the vicinity of the boundary of the space coordinate where the boundary condition of the first kind is given. This testifies that instantaneous heating (cooling) of the body up to the temperature of the environment is impossible in no circumstances of external heat exchange.