Selfsimilar expanders of the harmonic map flow

Pierre Germain; Melanie Rupflin

doi:10.1016/j.anihpc.2011.06.004

Selfsimilar expanders of the harmonic map flow

Pierre Germain, Melanie Rupflin

Mathematics

Research output: Contribution to journal › Article › peer-review

Abstract

We study the existence, uniqueness, and stability of self-similar expanders of the harmonic map heat flow in equivariant settings. We show that there exist selfsimilar solutions to any admissible initial data and that their uniqueness and stability properties are essentially determined by the energy-minimising properties of the so-called equator maps.

Original language	English (US)
Pages (from-to)	743-773
Number of pages	31
Journal	Annales de l'Institut Henri Poincare (C) Analyse Non Lineaire
Volume	28
Issue number	5
DOIs	https://doi.org/10.1016/j.anihpc.2011.06.004
State	Published - 2011

ASJC Scopus subject areas

Analysis
Mathematical Physics
Applied Mathematics

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10.1016/j.anihpc.2011.06.004

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title = "Selfsimilar expanders of the harmonic map flow",

abstract = "We study the existence, uniqueness, and stability of self-similar expanders of the harmonic map heat flow in equivariant settings. We show that there exist selfsimilar solutions to any admissible initial data and that their uniqueness and stability properties are essentially determined by the energy-minimising properties of the so-called equator maps.",

author = "Pierre Germain and Melanie Rupflin",

note = "Funding Information: * Corresponding author. Tel.: +44 (0)2476150774. E-mail address: M.Rupflin@warwick.ac.uk (M. Rupflin). 1 Partially supported by the Swiss National Science Foundation and The Leverhulme Trust.",

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PY - 2011

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N2 - We study the existence, uniqueness, and stability of self-similar expanders of the harmonic map heat flow in equivariant settings. We show that there exist selfsimilar solutions to any admissible initial data and that their uniqueness and stability properties are essentially determined by the energy-minimising properties of the so-called equator maps.

AB - We study the existence, uniqueness, and stability of self-similar expanders of the harmonic map heat flow in equivariant settings. We show that there exist selfsimilar solutions to any admissible initial data and that their uniqueness and stability properties are essentially determined by the energy-minimising properties of the so-called equator maps.

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Selfsimilar expanders of the harmonic map flow

Abstract

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