The second-order L2-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 L²-flow of inextensible elastic curves with hinged ends in the plane

Chun-Chi Lin, Yang-Kai Lue, Hartmut R. Schwetlick

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10 Citations (SciVal)

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
Early online date	12 Feb 2015
DOIs	https://doi.org/10.1007/s10659-015-9518-5
Publication status	Published - Apr 2015

Keywords

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

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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 - Lin, Chun-Chi

AU - Lue, Yang-Kai

AU - Schwetlick, Hartmut R.

PY - 2015/4

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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).

KW - Elastic energy

KW - Geometric flow

KW - Hinged boundary conditions

KW - Second-order parabolic equation

KW - Willmore functional

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EP - 291

JO - Journal of Elasticity

JF - Journal of Elasticity

IS - 1

ER -

The second-order L²-flow of inextensible elastic curves with hinged ends in the plane

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Hartmut Schwetlick

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The second-order L2-flow of inextensible elastic curves with hinged ends in the plane

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Hartmut Schwetlick

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The second-order L²-flow of inextensible elastic curves with hinged ends in the plane