Refined asymptotics for the blowup of ut — δu = up

This work is concerned with positive, blowing‐up solutions of the semilinear heat equation u t — δ u = u p in R n . Our main contribution is a sort of center manifold analysis for the equation in similarity variables, leading to refined asymptotics for u in a backward space‐time parabola near any blowup point. We also explore a connection between the asymptotics of u and the local geometry of the blowup set.