The motion of elastic planar closed curves under the area-preserving condition

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14 Citations (Scopus)

Abstract

We consider the motion of an elastic closed curve with constant enclosed area. This motion is governed by a system involving fourth order parabolic equations. We shall prove that this system has a unique classical solution for all time and the solution converges uniformly to a stationary solution together with its derivatives of any order.

Original languageEnglish
Pages (from-to)1871-1912
Number of pages42
JournalIndiana University Mathematics Journal
Volume56
Issue number4
DOIs
Publication statusPublished - 2007 Oct 29
Externally publishedYes

Keywords

  • Elastic energy
  • Gradient flow with two constraints
  • Isoperimetric inequality

ASJC Scopus subject areas

  • Mathematics(all)

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