## Abstract

We consider the Dirichlet problem for the energy-critical heat equation (Formula presented.) where Ω is a bounded smooth domain in R
^{3}. Let H
_{γ}(x,y) be the regular part of the Green function of -Δ-γ in Ω, where γ∈(0,λ
_{1}) and λ
_{1} is the first Dirichlet eigenvalue of -Δ. Then, given a point q∈Ω such that 3γ(q)<λ
_{1}, where (Formula presented.) we prove the existence of a non-radial global positive and smooth solution u(x, t) which blows up in infinite time with spike in q. The solution has the asymptotic profile (Formula presented.) where (Formula presented.)

Original language | English |
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Number of pages | 95 |

Journal | Mathematische Annalen |

Early online date | 15 May 2024 |

DOIs | |

Publication status | E-pub ahead of print - 15 May 2024 |