Infinite time blow-up for the 3D energy critical heat equation in bounded domains

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• Giacomo Ageno (Cambridge)
• Monday 29 January 2024, 14:00-15:00
• MR13.

If you have a question about this talk, please contact Zexing Li.

A positive solution to the Dirichlet problem for the energy-critical heat equation typically decays exponentially fast or blows up in finite time. In this talk, I will present the first examples of 3D global unbounded solutions without radial symmetry, precisely describing asymptotic behavior and stability. The dimension plays a crucial role, making the heart of the problem nonlocal and revealing a connection with the Brezis-Nirenberg problem. This is joint work with Manuel del Pino.

This talk is part of the Partial Differential Equations seminar series.

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