Analysis & PDE
- Anal. PDE
- Volume 13, Number 1 (2020), 215-274.
Infinite-time blow-up for the 3-dimensional energy-critical heat equation
We construct globally defined in time, unbounded positive solutions to the energy-critical heat equation in dimension 3
For each we find initial data (not necessarily radially symmetric) with such that as
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).
Anal. PDE, Volume 13, Number 1 (2020), 215-274.
Received: 22 April 2018
Accepted: 29 December 2018
First available in Project Euclid: 16 January 2020
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Mathematical Reviews number (MathSciNet)
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