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

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 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 Oct 29
Externally published	Yes

Keywords

Elastic energy
Gradient flow with two constraints
Isoperimetric inequality

ASJC Scopus subject areas

Mathematics(all)

Access to Document

10.1512/iumj.2007.56.3015

Fingerprint Dive into the research topics of 'The motion of elastic planar closed curves under the area-preserving condition'. Together they form a unique fingerprint.

Cite this

@article{c0f9ebead4cd43219b11d98bb914d9f9,

title = "The motion of elastic planar closed curves under the area-preserving condition",

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.",

keywords = "Elastic energy, Gradient flow with two constraints, Isoperimetric inequality",

author = "Shinya Okabe",

year = "2007",

month = oct,

day = "29",

doi = "10.1512/iumj.2007.56.3015",

language = "English",

volume = "56",

pages = "1871--1912",

journal = "Indiana University Mathematics Journal",

issn = "0022-2518",

publisher = "Indiana University",

number = "4",

}

TY - JOUR

T1 - The motion of elastic planar closed curves under the area-preserving condition

AU - Okabe, Shinya

PY - 2007/10/29

Y1 - 2007/10/29

N2 - 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.

AB - 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.

KW - Elastic energy

KW - Gradient flow with two constraints

KW - Isoperimetric inequality

UR - http://www.scopus.com/inward/record.url?scp=35448956427&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=35448956427&partnerID=8YFLogxK

U2 - 10.1512/iumj.2007.56.3015

DO - 10.1512/iumj.2007.56.3015

M3 - Article

AN - SCOPUS:35448956427

VL - 56

SP - 1871

EP - 1912

JO - Indiana University Mathematics Journal

JF - Indiana University Mathematics Journal

SN - 0022-2518

IS - 4

ER -