Convergence of Sobolev gradient trajectories to elastica (2107.06504v2)

Published 14 Jul 2021 in math.AP and math.DG

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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