Blow-up for a semilinear parabolic equation with large diffusion on R^N

We study the blow-up time and the location of the blow-up set of
the solution for a semilinear heat equation with large diffusive coefficient.
In particular, we prove that, if the diffusive coefficient is sufficiently lar
ge, then the location of the blow-up set depends on the large time behavior of
the hot spots of the solutions for the heat equation. This is a joint
work with Yohei Fujishima.