Dept. Math, Hokkaido Univ. EPrints Server

THE MOTION OF ELASTIC PLANAR CLOSED CURVES UNDER THE AREA-PRESERVING CONDITION

Preprint Series # 812
Okabe, Shinya THE MOTION OF ELASTIC PLANAR CLOSED CURVES UNDER THE AREA-PRESERVING CONDITION. (2006);

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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.

Item Type:Preprint
Subjects:49-xx CALCULUS OF VARIATIONS AND OPTIMAL CONTROL; OPTIMIZATION
35-xx PARTIAL DIFFERENTIAL EQUATIONS
ID Code:1634