## Analysis & PDE

• Anal. PDE
• Volume 13, Number 1 (2020), 215-274.

### Infinite-time blow-up for the 3-dimensional energy-critical heat equation

#### Abstract

We construct globally defined in time, unbounded positive solutions to the energy-critical heat equation in dimension 3

For each $γ>1$ we find initial data (not necessarily radially symmetric) with $lim|x|→∞|x|γu0(x)>0$ such that as $t→∞$

Furthermore we show that this infinite-time blow-up is codimensional-1 stable. The existence of such solutions was conjectured by Fila and King (Netw. Heterog. Media 7:4 (2012), 661–671).

#### Article information

Source
Anal. PDE, Volume 13, Number 1 (2020), 215-274.

Dates
Received: 22 April 2018
Accepted: 29 December 2018
First available in Project Euclid: 16 January 2020

Permanent link to this document
https://projecteuclid.org/euclid.apde/1579143672

Digital Object Identifier
doi:10.2140/apde.2020.13.215

Mathematical Reviews number (MathSciNet)
MR4047646

#### Citation

del Pino, Manuel; Musso, Monica; Wei, Juncheng. Infinite-time blow-up for the 3-dimensional energy-critical heat equation. Anal. PDE 13 (2020), no. 1, 215--274. doi:10.2140/apde.2020.13.215. https://projecteuclid.org/euclid.apde/1579143672

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