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2005 Asymptotic behaviors of star-shaped curves expanding by $V=1-K$
Hiroki Yagisita
Differential Integral Equations 18(2): 225-232 (2005).

Abstract

We consider asymptotic behaviors of star-shaped curves expanding by $V=1-K$, where $V$ denotes the outward-normal velocity and $K$ curvature. In this paper, we show the followings. The difference of the radial functions between an expanding curve and circle has its asymptotic shape as $t\rightarrow+\infty$. For two curves, if the asymptotic shapes are identical, then the curves are also. The set of all asymptotic shapes is dense in $C(S^1)$.

Citation

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Hiroki Yagisita. "Asymptotic behaviors of star-shaped curves expanding by $V=1-K$." Differential Integral Equations 18 (2) 225 - 232, 2005.

Information

Published: 2005
First available in Project Euclid: 21 December 2012

zbMATH: 1212.53094
MathSciNet: MR2106103

Subjects:
Primary: 53C44
Secondary: 35B30, 35B40

Rights: Copyright © 2005 Khayyam Publishing, Inc.

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Vol.18 • No. 2 • 2005
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