  The blow-up rate estimate for the solution to a semilinear parabolic equation
$u_t=\Delta u+V(x) |u|^{p-1}u$ in $\Omega \times (0,T)$ with 0-Dirichlet
boundary condition is obtained. As an application, it is shown that the
asymptotic behavior of blow-up time and blow-up set of the problem with
nonnegative initial data $u(x,0)=M\vf (x)$ as $M$ goes to infinity, which have
been found in \cite{cer}, are improved under some reasonable and weaker
conditions compared with \cite{cer}.
