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

^*Corresponding author for this work

Department of Mathematics

Research output: Contribution to journal › Article › peer-review

7 Citations (Scopus)

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).

Original language	English
Pages (from-to)	263-291
Number of pages	29
Journal	Journal of Elasticity
Volume	119
Issue number	1-2
DOIs	https://doi.org/10.1007/s10659-015-9518-5
Publication status	Published - 2015 Apr 1

Keywords

Elastic energy
Geometric flow
Hinged boundary conditions
Second-order parabolic equation
Willmore functional

ASJC Scopus subject areas

Materials Science(all)
Mechanics of Materials
Mechanical Engineering

Access to Document

10.1007/s10659-015-9518-5

Cite this

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

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).",

keywords = "Elastic energy, Geometric flow, Hinged boundary conditions, Second-order parabolic equation, Willmore functional",

author = "Lin, {Chun Chi} and Lue, {Yang Kai} and Schwetlick, {Hartmut R.}",

note = "Funding Information: During working on this project, C.-C. Lin was supported by the National Science Council of Taiwan NSC 101-2115-M-003-002 and the National Center for Theoretical Sciences in Taipei, Taiwan; and Y.-K. Lue was supported by MOST 103-2811-M-003-008. The authors also want to thank the referees for useful comments and corrections toward improving the presentation of this article. Publisher Copyright: {\textcopyright} 2015, Springer Science+Business Media Dordrecht.",

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N1 - Funding Information: During working on this project, C.-C. Lin was supported by the National Science Council of Taiwan NSC 101-2115-M-003-002 and the National Center for Theoretical Sciences in Taipei, Taiwan; and Y.-K. Lue was supported by MOST 103-2811-M-003-008. The authors also want to thank the referees for useful comments and corrections toward improving the presentation of this article. Publisher Copyright: © 2015, Springer Science+Business Media Dordrecht.

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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).

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