Below-threshold solutions of a focusing energy-critical heat equation in R4

Stephen Gustafson, Dimitrios Roxanas

Research output: Chapter in Book/Report/Conference proceedingChapter (peer-reviewed)peer-review

Abstract

We review recent results on the global well-posedness and decay versus blow-up and non-decay dichotomy, below the stationary solution, for a focusing energy-critical heat equation in R4: Our methods are inspired by recent progress towards the soliton resolution conjecture for dispersive and wave equations, providing an alternative way of studying critical parabolic problems.
Original languageEnglish
Title of host publicationNonlinear dispersive waves and fluids
Subtitle of host publicationAMS Proceedings in Contemporary Mathematics 2017-2018
PublisherAmerican Mathematical Society
Number of pages15
Publication statusAccepted/In press - 4 Jul 2018

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