  Some transformations acting on radially symmetric solutions to the following
class of non-homogeneous reaction-diffusion equations $$
|x|^{\sigma_1}\partial_tu=\Delta u^m+|x|^{\sigma_2}u^p, \qquad
(x,t)\in\real^N\times(0,\infty), $$ which has been proposed in a number of
previous mathematical works as well as in several physical models, are
introduced. We consider here $m\geq1$, $p\geq1$, $N\geq1$ and $\sigma_1$,
$\sigma_2$ real exponents. We apply these transformations in connection to
previous results on the one hand to deduce general qualitative properties of
radially symmetric solutions and on the other hand to construct self-similar
solutions which are expected to be patterns for the dynamics of the equations,
strongly improving the existing theory. We also introduce mappings between
solutions which work in the semilinear case $m=1$.
