Type II Blow-up in the 5-dimensional Energy Critical Heat Equation

被引：31

作者：

del Pino, Manuel ^{[1
,2
]}

Musso, Monica ^{[1
,3
]}

Wei, Jun Cheng ^{[4
]}

机构：

[1] Univ Bath, Dept Math Sci, Bath BA2 7AY, Avon, England

[2] Univ Chile, Dept Ingn Matemat CMM, Santiago 8370456, Chile

[3] Univ Catolica Chile, Dept Matemat, Macul 7820436, Chile

[4] Univ British Columbia, Dept Math, Vancouver, BC V6T 1Z2, Canada

来源：

ACTA MATHEMATICA SINICA-ENGLISH SERIES | 2019年 / 35卷 / 06期

基金：

加拿大自然科学与工程研究理事会;

关键词：

Singularity formation; bubbling phenomena; critical parabolic equations;

D O I：

10.1007/s10114-019-8341-5

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

We consider the Cauchy problem for the energy critical heat equation in dimension n = 5. More precisely we find that for given points q(1),q(2),...,q(k) and any sufficiently small T > 0 there is an initial condition u(0) such that the solution u(x,t) of (0.1) blows-up at exactly those k points with rates type II, namely with absolute size T-t)(-) for . The blow-up profile around each point is of bubbling type, in the form of sharply scaled Aubin-Talenti bubbles.

引用

页码：1027 / 1042

页数：16

共 24 条

[1]

Collot C., ARXIV160507337

[2]

Collot C., ARXIV170904941

[3] NONRADIAL TYPE II BLOW UP FOR THE ENERGY-SUPERCRITICAL SEMILINEAR HEAT EQUATION [J].