## Differential and Integral Equations

### Asymptotic behaviors of star-shaped curves expanding by $V=1-K$

Hiroki Yagisita

#### 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 $C(S^1)$.

#### Article information

Source
Differential Integral Equations, Volume 18, Number 2 (2005), 225-232.

Dates
First available in Project Euclid: 21 December 2012

Yagisita, Hiroki. Asymptotic behaviors of star-shaped curves expanding by $V=1-K$. Differential Integral Equations 18 (2005), no. 2, 225--232. https://projecteuclid.org/euclid.die/1356060230