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

Shinya Okabe

doi:10.1512/iumj.2007.56.3015

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

Shinya Okabe

Research output: Contribution to journal › Article › peer-review

15 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 language	English
Pages (from-to)	1871-1912
Number of pages	42
Journal	Indiana University Mathematics Journal
Volume	56
Issue number	4
DOIs	https://doi.org/10.1512/iumj.2007.56.3015
Publication status	Published - 2007
Externally published	Yes

Keywords

Elastic energy
Gradient flow with two constraints
Isoperimetric inequality

ASJC Scopus subject areas

Mathematics(all)

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10.1512/iumj.2007.56.3015

Cite this

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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.",

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KW - Elastic energy

KW - Gradient flow with two constraints

KW - Isoperimetric inequality

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

Abstract

Keywords

ASJC Scopus subject areas

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