  We study global in time existence versus blow-up in finite time of solutions
to the Cauchy problem for the porous medium equation with a variable density
$\rho(x)$ and a power-like reaction term posed in the one dimensional interval
$(-R,R)$, $R>0$. Here the weight function is singular at the boundary of the
domain $(-R,R)$, indeed it is such that $\rho(x)\sim (R-|x|)^{-q}$ as $|x|\to
R$, with $q\ge0$. We show a different behavior of solutions depending on the
three cases when $q>2$, $q=2$ and $q<2$.
