Vol. 13, No. 1, 2020

Download this article
Download this article For screen
For printing
Recent Issues

Volume 14
Issue 6, 1671–1976
Issue 5, 1333–1669
Issue 4, 985–1332
Issue 3, 667–984
Issue 2, 323–666
Issue 1, 1–322

Volume 13, 8 issues

Volume 12, 8 issues

Volume 11, 8 issues

Volume 10, 8 issues

Volume 9, 8 issues

Volume 8, 8 issues

Volume 7, 8 issues

Volume 6, 8 issues

Volume 5, 5 issues

Volume 4, 5 issues

Volume 3, 4 issues

Volume 2, 3 issues

Volume 1, 3 issues

The Journal
About the Journal
Editorial Board
Editors’ Interests
Subscriptions
 
Submission Guidelines
Submission Form
Policies for Authors
Ethics Statement
 
ISSN: 1948-206X (e-only)
ISSN: 2157-5045 (print)
Author Index
To Appear
 
Other MSP Journals
This article is available for purchase or by subscription. See below.
Infinite-time blow-up for the 3-dimensional energy-critical heat equation

Manuel del Pino, Monica Musso and Juncheng Wei

Vol. 13 (2020), No. 1, 215–274
Abstract

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

ut = Δu + u5 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) tγ1 2  if 1 < γ < 2,u(,t)t if γ > 2,u(,t)t(lnt)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).

PDF Access Denied

However, your active subscription may be available on Project Euclid at
https://projecteuclid.org/apde

We have not been able to recognize your IP address 52.23.219.12 as that of a subscriber to this journal.
Online access to the content of recent issues is by subscription, or purchase of single articles.

Please contact your institution's librarian suggesting a subscription, for example by using our journal-recom­mendation form. Or, visit our subscription page for instructions on purchasing a subscription.

You may also contact us at contact@msp.org
or by using our contact form.

Or, you may purchase this single article for USD 40.00:

Keywords
blow-up, critical exponents, nonlinear parabolic equations
Mathematical Subject Classification 2010
Primary: 35B33, 35B40, 35K58
Milestones
Received: 22 April 2018
Accepted: 29 December 2018
Published: 6 January 2020
Authors
Manuel del Pino
Department of Mathematical Sciences
University of Bath
Bath
United Kingdom
Monica Musso
Department of Mathematical Sciences
University of Bath
Bath
United Kingdom
Juncheng Wei
Department of Mathematics
University of British Columbia
Vancouver, BC
Canada