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Abstract
We consider the Cauchy problem for the energy critical heat equation {ut=Δu+u4n−2uinRn×(0,T)u(⋅,0)=u0inRn 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) blowsup at exactly those k points with rates type II, namely with absolute size ~(Tt) ^{α} for α > 34. The blowup profile around each point is of bubbling type, in the form of sharply scaled Aubin–Talenti bubbles.
Original language  English 

Pages (fromto)  10271042 
Number of pages  16 
Journal  Acta Mathematica Sinica, English Series 
Volume  35 
Issue number  6 
Early online date  20 May 2019 
DOIs  
Publication status  Published  1 Jun 2019 
Keywords
 35B40
 35K58
 bubbling phenomena
 critical parabolic equations
 Singularity formation
ASJC Scopus subject areas
 Mathematics(all)
 Applied Mathematics
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Projects
 1 Active

Concentration phenomena in nonlinear analysis
Engineering and Physical Sciences Research Council
27/04/20 → 26/04/23
Project: Research council