Analytic solutions of the nonlinear radiation diffusion equation with an instantaneous point source in non-homogeneous media

Analytic solutions to the nonlinear radiation diffusion equation with an instantaneous point source for a non-homogeneous medium power law spatial density profile, are presented. The generalization of well known homogeneous medium. It is shown that take various qualitatively different forms according value exponent. These studied in detail linear and non heat conduction. In addition, by inspecting generalized solutions, we show there exist values exponent such conduction front has constant speed or even accelerates. Finally, solution compared numerical simulations, good agreement achieved.