Existence and convergence of the length-preserving elastic flow of clamped curves

Fabian Rupp, Adrian Spener

Publications: Contribution to journalArticlePeer Reviewed

Abstract

We study the evolution of curves with fixed length and clamped boundary conditions moving by the negative L2-gradient flow of the elastic energy. For any initial curve lying merely in the energy space we show existence and parabolic smoothing of the solution. Applying previous results on long-time existence and proving a constrained Łojasiewicz–Simon gradient inequality we furthermore show convergence to a critical point as time tends to infinity.

Original languageEnglish
Article number59
JournalJournal of Evolution Equations
Volume24
Issue number3
DOIs
Publication statusPublished - Sept 2024

Austrian Fields of Science 2012

  • 101002 Analysis
  • 101006 Differential geometry
  • 101028 Mathematical modelling
  • 101027 Dynamical systems

Keywords

  • 35K55
  • Clamped boundary conditions
  • Elastic energy
  • Nonlocal geometric evolution equation
  • Primary 53E40
  • Secondary 35K52
  • Willmore functional
  • Łojasiewicz–Simon gradient inequality

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