Non-accessible singular homoclinic orbits for a semilinear parabolic equation

Abstract

We show the existence of at least three different continuations beyond blow-up for a backward self-similar solution of a supercritical Fujita equation. One of these extended solutions cannot be approximated by classical entire solutions in a specific way given by the scaling invariance of the equation, while the minimal continuation is known to be accessible by a family of such entire solutions.