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

作     者：Manuel del PINO Monica MUSSO Jun Cheng WEI 

作者机构：Department of Mathematical Sciences University of Bath Departamento de Ingeniería Matemática-CMM Universidad de Chile Departamento de Matemáticas Universidad Católica de Chile Department of Mathematics University of British Columbia 

出 版 物：《Acta Mathematica Sinica,English Series》 (数学学报（英文版）)

年 卷 期：2019年第35卷第6期

页      面：1027-1042页

核心收录：

学科分类：07[理学] 070104[理学-应用数学] 0701[理学-数学] 

基　　金：supported by a UK Royal Society Research Professorship and Fondo Basal CMM-Chile partly supported by grants Fondecyt 1160135,Chile partially supported by NSERC of Canada 

主　　题：Singularity formation bubbling phenomena critical parabolic equations 

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 u0 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)^(-α) for α 3/4. The blow-up profile around each point is of bubbling type, in the form of sharply scaled Aubin–Talenti bubbles.