Partial differential equations
Stability of ODE blow-up for the energy critical semilinear heat equation

Presented by: Jean-Michel Coron

Collot, Charles1; Merle, Frank2, 3; Raphaël, Pierre1
1 Laboratoire Jean-Alexandre-Dieudonné, Université de Nice–Sophia Antipolis, France
2 Laboratoire Laga, Université de Cergy-Pontoise, France
3 IHES, Bures-sur-Yvette, France
Comptes Rendus. Mathématique, Volume 355 (2017) no. 1, pp. 65-79.

We consider the energy critical semilinear heat equation

∂tu=Δu+|u|4d−2u,x∈Rd
in dimension d≥3. We propose a self-contained proof of the stability of solutions u blowing-up in finite time with type-I ODE blow-up
‖u‖L∞∼κ(T−t)d−24,T>0,κ:=(d−24)d−24
which adapts to the energy critical case the proof of Fermanian, Merle, Zaag [4].

Nous considérons l'équation de la chaleur énergie critique

∂tu=Δu+|u|4d−2u,x∈Rd
en dimension d≥3. Nous proposons une preuve auto-contenue de la stabilité du régime explosif de type EDO
‖u‖L∞∼κ(T−t)d−24,T>0,κ:=(d−24)d−24
qui adapte au cas énergie critique la preuve de Fermanian, Merle, Zaag [4].

Received:
Accepted:
Published online:
DOI: 10.1016/j.crma.2016.10.020
Collot, Charles 1; Merle, Frank 2, 3; Raphaël, Pierre 1

1 Laboratoire Jean-Alexandre-Dieudonné, Université de Nice–Sophia Antipolis, France
2 Laboratoire Laga, Université de Cergy-Pontoise, France
3 IHES, Bures-sur-Yvette, France 
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Collot, Charles; Merle, Frank; Raphaël, Pierre. Stability of ODE blow-up for the energy critical semilinear heat equation. Comptes Rendus. Mathématique, Volume 355 (2017) no. 1, pp. 65-79. doi : 10.1016/j.crma.2016.10.020. https://www.numdam.org/articles/10.1016/j.crma.2016.10.020/

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