Blow-up for a semilinear parabolic equation with large diffusion on RN

We consider the Cauchy problem for a semilinear heat equation, where D>0, p>1, N 3, λ>0, and . In this paper we assume and study the blow-up time and the location of the blow-up set of the solution for the case where D is sufficiently large. In particular, we prove that the location of the blow-up set depends on the large time behavior of the hot spots for the heat equation.