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).
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