| Abstract: |
| A positive solution to the Dirichlet problem for the energy-critical heat equation typically decays exponentially fast or blows up in finite time. Threshold behaviors between these two scenarios exist, having been studied since the 1980s. In this talk, I will introduce the first examples of global, unbounded solutions without radial symmetry, precisely describing
asymptotic and stability. The low dimension $\{3,4\}$ plays a crucial role, making the heart of the problem nonlocal. In dimension $3$ the analysis reveals a connection with the Brezis-Nirenberg number.
This is joint work with Manuel del Pino. |
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