Convergence of Sobolev gradient trajectories to elastica

2021/07/14 by Shinya Okabe, Okabe, Shinya, Philip Schrader +1
Mathematics · Computer Science · #Geometric Analysis and Curvature Flows #Nonlinear Partial Differential Equations #Advanced Mathematical Modeling in Engineering

paper · pdf · doi:10.48550/arxiv.2107.06504

Abstract

In this paper we study the H²(ds)-gradient flow for the modified elastic energy defined on closed curves in ℝⁿ. 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.

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