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 journalArticlepeer-review

3 Citations (Scopus)


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
Issue number1-2
Publication statusPublished - 2015 Apr 1


  • 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


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