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