Fila, Marek; Yanagida, Eiji Non-accessible singular homoclinic orbits for a semilinear parabolic equation. (English) Zbl 1340.35179 Differ. Integral Equ. 27, No. 5-6, 563-578 (2014). 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. Cited in 2 Documents MSC: 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 Keywords:Fujita equation; positive solutions; accessible element × Cite Format Result Cite Review PDF