Convergence of Sobolev gradient trajectories to elastica

Shinya Okabe; Philip Schrader

Convergence of Sobolev gradient trajectories to elastica

Analysis of PDEs 2023-01-30 v2 Differential Geometry

Authors: Shinya Okabe , Philip Schrader

Abstract

In this paper we study the $H^2(ds)$ -gradient flow for the modified elastic energy defined on closed curves in $\mathbb{R}^n$ . We prove the existence of a unique global-in-time solution to the flow and establish full convergence to elastica by way of a {\L}ojasiewicz--Simon gradient inequality.

Keywords

sobolev gradient flow elastic energy elastica lojasiewicz-simon inequality closed curves

Cite

@article{arxiv.2107.06504,
  title  = {Convergence of Sobolev gradient trajectories to elastica},
  author = {Shinya Okabe and Philip Schrader},
  journal= {arXiv preprint arXiv:2107.06504},
  year   = {2023}
}

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