  The phenomenon of finite time extinction of bounded and non-negative
solutions to the diffusion equation with strong absorption $$\partial_t
u-\Delta u^m+|x|^{\sigma}u^q=0, \qquad (t,x)\in(0,\infty)\times\mathbb{R}^N,$$
with $m\geq1$, $q\in(0,1)$ and $\sigma>0$, is addressed. Introducing the
critical exponent $\sigma^* := 2(1-q)/(m-1)$ for $m>1$ and $\sigma_*=\infty$
for $m=1$, extinction in finite time is known to take place for $\sigma\in
[0,\sigma^*)$ and an alternative proof is provided therein. When $m>1$ and
$\sigma\ge \sigma^*$, the occurrence of finite time extinction is proved for a
specific class of initial conditions, thereby supplementing results on
non-extinction that are available in that range of $\sigma$ and showing their
sharpness.
