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2020 Infinite-time blow-up for the 3-dimensional energy-critical heat equation
Manuel del Pino, Monica Musso, Juncheng Wei
Anal. PDE 13(1): 215-274 (2020). DOI: 10.2140/apde.2020.13.215

Abstract

We construct globally defined in time, unbounded positive solutions to the energy-critical heat equation in dimension 3

u t = Δ u + u 5  in  3 × ( 0 , ) , u ( x , 0 ) = u 0 ( x )  in  3 .

For each γ>1 we find initial data (not necessarily radially symmetric) with lim|x||x|γu0(x)>0 such that as t

u ( , t ) t γ 1 2  if  1 < γ < 2 , u ( , t ) t  if  γ > 2 , u ( , t ) t ( ln t ) 1  if  γ = 2 .

Furthermore we show that this infinite-time blow-up is codimensional-1 stable. The existence of such solutions was conjectured by Fila and King (Netw. Heterog. Media 7:4 (2012), 661–671).

Citation

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Manuel del Pino. Monica Musso. Juncheng Wei. "Infinite-time blow-up for the 3-dimensional energy-critical heat equation." Anal. PDE 13 (1) 215 - 274, 2020. https://doi.org/10.2140/apde.2020.13.215

Information

Received: 22 April 2018; Accepted: 29 December 2018; Published: 2020
First available in Project Euclid: 16 January 2020

zbMATH: 07171993
MathSciNet: MR4047646
Digital Object Identifier: 10.2140/apde.2020.13.215

Subjects:
Primary: 35B33 , 35B40 , 35K58

Keywords: Blow-up , Critical exponents , nonlinear parabolic equations

Rights: Copyright © 2020 Mathematical Sciences Publishers

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