We study here the blow-up set of the maximal classical
$u_t -\Delta u = g(u)$ on a ball of $\mathbb R^N$, $N \geq 2$
for a large class of nonlinearities $g$, with
$u(x,0) = u_0(|x|)$.
Numerical experiments show the interesting behaviour of the
blow-up set in respect of $u_0$.
As a theoretical background
to the method used
in this work, we prove an
important monotonicity property,
that is for a fixed
positive radius $r_0$, when the solution gets large enough at a certain time $t_0$,
then $u$ is monotone increasing at $r_0$ after $t_0$.
Finally, a single radius blow-up
property is proved for some large initial conditions.