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 |
|---|---|
| Article number | 111420 |
| Pages (from-to) | 1-94 |
| Number of pages | 94 |
| Journal | Mathematische Annalen |
| Volume | 391 |
| Issue number | 1 |
| Early online date | 15 May 2024 |
| DOIs | |
| Publication status | E-pub ahead of print - 15 May 2024 |
Acknowledgements
The authors express gratitude to the anonymous referee for their careful reading, which contributed to the improvement of the manuscript.Funding
The authors acknowledge the support from the Royal Society Research Professorship RP-R1-180114, United Kingdom. G. Ageno acknowledges support from the ERC/UKRI 2208 Horizon Europe Grant SWAT EP/X030644/1 and M. del Pino from the ERC/UKRI Horizon Europe Grant ASYMEVOL EP/Z000394/1. The authors express gratitude to the anonymous referee for their careful reading, which contributed to the improvement of the manuscript.
| Funders | Funder number |
|---|---|
| European Research Council | |
| Royal Society | RP-R1-180114 |
| Royal Society | |
| UKRI 2208 Horizon Europe | SWAT EP/X030644/1 |
| UKRI Horizon Europe | ASYMEVOL EP/Z000394/1 |
