The Second-Order L        2-Flow of Inextensible Elastic Curves with Hinged Ends in the Plane

Chun Chi Lin; Yang Kai Lue; Hartmut R. Schwetlick

doi:10.1007/s10659-015-9518-5

The Second-Order L ²-Flow of Inextensible Elastic Curves with Hinged Ends in the Plane

Chun Chi Lin^*
, Yang Kai Lue
, Hartmut R. Schwetlick

^*此作品的通信作者

數學系

研究成果: 雜誌貢獻 › 期刊論文 › 同行評審

13 引文斯高帕斯（Scopus）

摘要

In this article, we study the evolution of open inextensible planar curves with hinged ends. We obtain long time existence of C^∞-smooth solutions during the evolution, given the initial curves that are only C²-smooth with vanishing curvature at the boundary. Moreover, the asymptotic limits of this flow are inextensible elasticae. Our method and result extend the work by Wen (Duke Math. J. 70(3):683–698, 1993).

原文	英語
頁（從 - 到）	263-291
頁數	29
期刊	Journal of Elasticity
卷	119
發行號	1-2
DOIs	https://doi.org/10.1007/s10659-015-9518-5
出版狀態	已發佈 - 2015 4月 1

ASJC Scopus subject areas

一般材料科學
材料力學
機械工業

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10.1007/s10659-015-9518-5

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abstract = "In this article, we study the evolution of open inextensible planar curves with hinged ends. We obtain long time existence of C∞-smooth solutions during the evolution, given the initial curves that are only C2-smooth with vanishing curvature at the boundary. Moreover, the asymptotic limits of this flow are inextensible elasticae. Our method and result extend the work by Wen (Duke Math. J. 70(3):683–698, 1993).",

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AU - Lue, Yang Kai

AU - Schwetlick, Hartmut R.

PY - 2015/4/1

Y1 - 2015/4/1

N2 - In this article, we study the evolution of open inextensible planar curves with hinged ends. We obtain long time existence of C∞-smooth solutions during the evolution, given the initial curves that are only C2-smooth with vanishing curvature at the boundary. Moreover, the asymptotic limits of this flow are inextensible elasticae. Our method and result extend the work by Wen (Duke Math. J. 70(3):683–698, 1993).

AB - In this article, we study the evolution of open inextensible planar curves with hinged ends. We obtain long time existence of C∞-smooth solutions during the evolution, given the initial curves that are only C2-smooth with vanishing curvature at the boundary. Moreover, the asymptotic limits of this flow are inextensible elasticae. Our method and result extend the work by Wen (Duke Math. J. 70(3):683–698, 1993).

KW - Elastic energy

KW - Geometric flow

KW - Hinged boundary conditions

KW - Second-order parabolic equation

KW - Willmore functional

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IS - 1-2

ER -

The Second-Order L 2-Flow of Inextensible Elastic Curves with Hinged Ends in the Plane

摘要

ASJC Scopus subject areas

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The Second-Order L ²-Flow of Inextensible Elastic Curves with Hinged Ends in the Plane