This paper is concerned with the initial boundary value problem
[GRAPHICS]
where p > 1, epsilon > 0, Omega is a bounded domain in R-N, and phi is a co
ntinuous function on fl. It is shown that the blowup time T(epsilon) of the
solution of this problem satisfies T(epsilon) --> 1/p-1\phi\(1-p)(infinity
) as epsilon --> 0. Moreover, when the maximum of \phi (x)\ is attained at
one point, we determine the higher order term of T(epsilon) which reflects
the pointedness of the peak of \phi\. The proof is based on a careful const
ruction of super- and subsolutions. (C) 2001 Academic Press.