Blow-up set for a semilinear heat equation with small diffusion

We consider the blow-up problem for a semilinear heat equation, where Ω is a domain in RN, N 1, >0, p>1, and T>0. In this paper, under suitable assumptions on {φ }, we prove that, if the family of the solutions {u } satisfies a uniform type I blow-up estimate with respect to , then the solution u blows up only near the maximum points of the initial datum φ for any sufficiently small >0. This is proved without any conditions on the exponent p and the domain Ω, such as (N−2)p