Life span of solutions for a semilinear parabolic problem with small diffusion

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 continuous 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 construction of super- and subsolutions. (C) 2001 Academic Press.