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arXiv · 2107.06504

Convergence of Sobolev gradient trajectories to elastica

Shinya Okabe·Philip Schrader
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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.

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Shinya Okabe, Philip Schrader. 2021-07-14. Convergence of Sobolev gradient trajectories to elastica. https://doi.org/10.4310/cag.251005170853

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