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

被引：5

作者：

Collot, Charles ^{[1
]}

Merle, Frank ^{[2
,3
]}

Raphael, Pierre ^{[1
]}

机构：

[1] Univ Nice Sophia Antipolis, Lab Jean Alexandre Dieudonne, Nice, France

[2] Univ Cergy Pontoise, Lab Laga, Cergy Pontoise, France

[3] IHES, Bures Sur Yvette, France

来源：

COMPTES RENDUS MATHEMATIQUE | 2017年 / 355卷 / 01期

基金：

欧洲研究理事会;

关键词：

D O I：

10.1016/j.crma.2016.10.020

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

We consider the energy critical semilinear heat equation partial derivative(t)u = Delta u + vertical bar u vertical bar(4/d-2)u, x is an element of R-d 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 parallel to u parallel to(infinity)(L) similar to k(T-t)(d-2/4), T > 0, k := (d-2/4)(d-2/4) which adapts to the energy critical case the proof of Fermanian, Merle, Zaag [4]. (C) 2016 Acadamie des sciences. Published by Elsevier Masson SAS.

引用

页码：65 / 79

页数：15

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