self-similar solution of the radiation heat wave equation: diffusion from an instantaneous point source

Radiation heat waves play important roles in plasma physics, and in particular in inertial confinement fusion. the hydrodynamic equations with nonlinear conduction when the internal energy and the opacity have power-law dependences in the density and in the temperature are considered. the self-similar solution can exhibit a shock wave followed by an ablation front if the surface temperature does not increase too fast in time. results indicate that the diffusion from an instantaneous point source, also known as the nonlinear heat conduction.