#### Vol. 13, No. 1, 2020

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

### Manuel del Pino, Monica Musso and Juncheng Wei

Vol. 13 (2020), No. 1, 215–274
##### Abstract

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

For each $\gamma >1$ we find initial data (not necessarily radially symmetric) with $\underset{|x|\to \infty }{lim}|x{|}^{\gamma }{u}_{0}\left(x\right)>0$ such that as $t\to \infty$

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).

##### Keywords
blow-up, critical exponents, nonlinear parabolic equations
##### Mathematical Subject Classification 2010
Primary: 35B33, 35B40, 35K58