Curve shortening-straightening flow for non-closed planar curves with infinite length

Matteo Novaga, Shinya Okabe

Research output: Contribution to journalArticlepeer-review

10 Citations (Scopus)

Abstract

We consider a motion of non-closed planar curves with infinite length. The motion is governed by a steepest descent flow for the geometric functional which consists of the sum of the length functional and the total squared curvature. We call the flow shortening-straightening flow. In this paper, first we prove a long time existence result for the shortening-straightening flow for non-closed planar curves with infinite length. Then we show that the solution converges to a stationary solution as time goes to infinity. Moreover we give a classification of the stationary solution.

Original languageEnglish
Pages (from-to)1093-1132
Number of pages40
JournalJournal of Differential Equations
Volume256
Issue number3
DOIs
Publication statusPublished - 2014 Feb 1

Keywords

  • Elastic curves
  • Fourth order equations
  • Geometric evolution equations

ASJC Scopus subject areas

  • Analysis
  • Applied Mathematics

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