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Abstract
We construct globally defined in time, unbounded positive solutions to the energycritical heat equation in dimension 3 u_{t} = Δ u + u^{5} in R^{3} × (0, ∞), u(x, 0) = u_{0}(x) in R^{3}. For each γ > 1 we find initial data (not necessarily radially symmetric) with lim x → ∞ x γ u_{0} (x) > 0 such that as t → ∞ u (·, t)  ∞ ~ tγ1/2 if 1 < γ < 2, u (·, t)  ∞ ~ √t if γ > 2, u (·, t)  ∞ ~ √t(Int) ^{1} if γ = 2. Furthermore we show that this infinitetime blowup is codimensional1 stable. The existence of such solutions was conjectured by Fila and King.
Original language  English 

Pages (fromto)  215274 
Number of pages  60 
Journal  Analysis and PDE 
Volume  13 
Issue number  1 
DOIs  
Publication status  Published  6 Jan 2020 
Keywords
 Blowup
 Critical exponents
 Nonlinear parabolic equations
ASJC Scopus subject areas
 Analysis
 Numerical Analysis
 Applied Mathematics
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Dive into the research topics of 'Infinitetime blowup for the 3dimensional energycritical heat equation'. Together they form a unique fingerprint.Projects
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Concentration phenomena in nonlinear analysis
Engineering and Physical Sciences Research Council
27/04/20 → 31/03/24
Project: Research council