Existence and convergence of the length-preserving elastic flow of clamped curves

IF 1.1 3区数学 Q1 MATHEMATICS

Journal of Evolution Equations Pub Date : 2024-07-02 DOI:10.1007/s00028-024-00988-1

Fabian Rupp, Adrian Spener

引用次数: 0

Abstract

We study the evolution of curves with fixed length and clamped boundary conditions moving by the negative \(L^2\)-gradient flow of the elastic energy. For any initial curve lying merely in the energy space we show existence and parabolic smoothing of the solution. Applying previous results on long-time existence and proving a constrained Łojasiewicz–Simon gradient inequality we furthermore show convergence to a critical point as time tends to infinity.

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夹紧曲线的保长弹性流的存在性和收敛性

我们研究了具有固定长度和夹紧边界条件的曲线在弹性能量的负\(L^2\)梯度流作用下的演化。对于仅仅位于能量空间的任何初始曲线，我们都证明了解的存在性和抛物线平滑性。应用之前关于长时间存在性的结果，并证明受约束的 Łojasiewicz-Simon 梯度不等式，我们进一步证明了随着时间趋于无穷，临界点的收敛性。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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来源期刊

Journal of Evolution Equations 数学-数学

CiteScore

2.30

自引率

7.10%

发文量

审稿时长

>12 weeks

期刊介绍： The Journal of Evolution Equations (JEE) publishes high-quality, peer-reviewed papers on equations dealing with time dependent systems and ranging from abstract theory to concrete applications. Research articles should contain new and important results. Survey articles on recent developments are also considered as important contributions to the field. Particular topics covered by the journal are: Linear and Nonlinear Semigroups Parabolic and Hyperbolic Partial Differential Equations Reaction Diffusion Equations Deterministic and Stochastic Control Systems Transport and Population Equations Volterra Equations Delay Equations Stochastic Processes and Dirichlet Forms Maximal Regularity and Functional Calculi Asymptotics and Qualitative Theory of Linear and Nonlinear Evolution Equations Evolution Equations in Mathematical Physics Elliptic Operators