Refined asymptotics for the blowup of <i>u_t</i> — δ<i>u</i> = <i>u</i>^p

Abstract

Abstract 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.