  We classify all the blow-up solutions in self-similar form to the following
reaction-diffusion equation $$ \partial_tu=\Delta u^m+|x|^{\sigma}u^p, $$ posed
for $(x,t)\in\real^N\times(0,T)$, with $m>1$, $1\leq p<m$ and
$-2(p-1)/(m-1)<\sigma<\infty$. We prove that there are several types of
self-similar solutions with respect to the local behavior near the origin, and
their existence depends on the magnitude of $\sigma$. In particular, these
solutions have different blow-up sets and rates: some of them have $x=0$ as a
blow-up point, some other only blow up at (space) infinity. We thus emphasize
on the effect of the weight on the specific form of the blow-up patterns of the
equation. The present study generalizes previous works by the authors limited
to dimension $N=1$ and $\sigma>0$.
