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

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• 作者：Charles Collot^a ; ^{ccollot@unice.fr} ; Frank Merle^b ; ^c ; ^{merle@math.ucergy.fr} ; Pierre Raphaë ; l^a ; ^{praphael@unice.fr}
• 刊名：Comptes Rendus Mathematique
• 出版年：2017
• 出版时间：January 2017
• 年：2017
• 卷：355
• 期：1
• 页码：65-79
• 全文大小：431 K
• 卷排序：355

文摘

We consider the energy critical semilinear heat equation∂tu=Δu+|u|4d−2u,x∈Rd in dimension d≥3d≥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].