Stability of ODE blow-up for the energy critical semilinear heat equation
type: Item
instance of: scholarly article
title: Stability of ODE blow-up for the energy critical semilinear heat equation
zbMATH Open document ID: 1364.35156
author: Charles Collot
author: Frank Merle
author: P. Raphaël
published in: Comptes Rendus. Mathématique. Académie des Sciences, Paris
publication date: 2017-01-10T00:00:00Z
review text: The authors consider the energy critical semilinear heat equation \[ \begin{cases} \partial_t u =\Delta u +|u|^{p-1}u, \;p=\frac{d+2}{d-2} & (t,x)\in{\mathbb R}\times{\mathbb R}^d, d\geq 3,\\ u(0,x)=u_0(x)\in {\mathbb R}.\end{cases} \] They give a self-contained proof of the stability of solutions \(u\) blowing up in finite time with type-I ODE blow-up \[ \|u\|_{L^\infty}\sim k(T-t)^{\frac{d-2}{4}}, \;T>0, \;k=\big( \frac{d-2}{4} \big)^{\frac{d-2}4}, \] which adapts to the energy critical case. It is proved that e set of solutions blowing up in finite time with type-I blow-up is open in \(W^{3,\infty}({\mathbb R}^d).\)
Mathematics Subject Classification ID: 35K58
Mathematics Subject Classification ID: 35B44
zbMATH DE Number: 6673226
zbMATH Keywords: semilinear heat equations, blow-up solutions
reviewed by: Lubomira Softova
MaRDI profile type: Publication
full work available at URL: j.crma.2016.10.020
OpenAlex ID: W2551007572
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DOI: 10.1016/J.CRMA.2016.10.020
description: scientific article; zbMATH DE number 6673226