Key points are not available for this paper at this time.
We classify the smooth linearly stable self-similar solutions of the semilinear heat equation uₜ= u+|u|^p-1u in Rⁿ (0, T) under an integral condition for all p>1. As a corollary, we prove that finite time blowing up solutions of this equation on a bounded convex domain with u (, 0) 0 and uₜ (, 0) 0 converges to a constant after rescaling at the blow-up point for all p>1.
Choi et al. (Mon,) studied this question.