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Non-accessible singular homoclinic orbits for a semilinear parabolic equation. (English) Zbl 1340.35179
Summary: 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.
Reviewer: Reviewer (Berlin)

35K91 Semilinear parabolic equations with Laplacian, bi-Laplacian or poly-Laplacian
35B05 Oscillation, zeros of solutions, mean value theorems, etc. in context of PDEs
35B44 Blow-up in context of PDEs
37C29 Homoclinic and heteroclinic orbits for dynamical systems
35B09 Positive solutions to PDEs
35B60 Continuation and prolongation of solutions to PDEs