Convergence of Sobolev gradient trajectories to elastica

Shinya Okabe; Philip Schrader

doi:10.4310/CAG.251005170853

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Convergence of Sobolev gradient trajectories to elastica

Journal article

Peer reviewed

Convergence of Sobolev gradient trajectories to elastica

Shinya Okabe and Philip Schrader

Communications in analysis and geometry, Vol.33(5), pp.1199-1242

2025

DOI: https://doi.org/10.4310/CAG.251005170853

Abstract

In this paper we study the H2(ds)-gradient flow for the modified elastic energy defined on closed immersed curves in. We prove the existence of a unique global-in-time solution to the flow and establish full convergence to elastica by way of a Łojasiewicz-Simon gradient inequality.

Details

Title: Convergence of Sobolev gradient trajectories to elastica
Authors/Creators: Shinya Okabe - Tohoku University
Philip Schrader - Murdoch University
Publication Details: Communications in analysis and geometry, Vol.33(5), pp.1199-1242
Publisher: International Press
Number of pages: 44
Identifiers: 991005829749807891
Murdoch Affiliation: School of Mathematics, Statistics, Chemistry and Physics
Language: English
Resource Type: Journal article

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Collaboration types: Domestic collaboration; International collaboration
Citation topics: 9 Mathematics; 9.50 Applied Statistics & Probability; 9.50.415 Harmonic Maps
Web Of Science research areas: Mathematics
ESI research areas: Mathematics