  Let $\Omega$ be a bounded smooth domain in $\RR^N$. We consider the problem
$u_t= \Delta u + V(x) u^p$ in $\Omega \times [0,T)$, with Dirichlet boundary
conditions $u=0$ on $\partial \Omega \times [0,T)$ and initial datum $u(x,0)= M
\phi (x)$ where $M \geq 0$, $\phi$ is positive and compatible with the boundary
condition. We give estimates for the blow up time of solutions for large values
of $M$. As a consequence of these estimates we find that, for $M$ large, the
blow up set concentrates near the points where $\phi^{p-1}V$ attains its
maximum.
