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

Research output: Contribution to journalArticle

2 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 languageEnglish
Pages (from-to)263-291
Number of pages29
JournalJournal of Elasticity
Volume119
Issue number1-2
DOIs
Publication statusPublished - 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

Cite this

The Second-Order L 2-Flow of Inextensible Elastic Curves with Hinged Ends in the Plane. / Lin, Chun-Chi; Lue, Yang Kai; Schwetlick, Hartmut R.

In: Journal of Elasticity, Vol. 119, No. 1-2, 01.04.2015, p. 263-291.

Research output: Contribution to journalArticle

Lin, Chun-Chi ; Lue, Yang Kai ; Schwetlick, Hartmut R. / The Second-Order L 2-Flow of Inextensible Elastic Curves with Hinged Ends in the Plane. In: Journal of Elasticity. 2015 ; Vol. 119, No. 1-2. pp. 263-291.
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