L 2-flow of elastic curves with clamped boundary conditions

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Abstract

In this paper we investigate the L 2-flow of elastic curves with clamped boundary conditions in n-dimensional Euclidean spaces. The L 2-flow corresponds to a fourth-order parabolic equation. In the case of closed curves, the long-time existence of solutions of this evolution equation has been derived in the literature. We extend this result to the case of open (i.e., non-closed) curves with clamped boundary conditions.

Original languageEnglish
Pages (from-to)6414-6428
Number of pages15
JournalJournal of Differential Equations
Volume252
Issue number12
DOIs
Publication statusPublished - 2012 Jun 15

Keywords

  • Clamped boundary condition
  • Elastic curve
  • Fourth-order flow

ASJC Scopus subject areas

  • Analysis
  • Applied Mathematics

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