The self-similar expanding curve for the curvature flow equation

Authors:
Hua-Huai Chern, Jong-Shenq Guo and Chu-Pin Lo

Journal:
Proc. Amer. Math. Soc. **131** (2003), 3191-3201

MSC (2000):
Primary 35B60, 34A12, 35B35

DOI:
https://doi.org/10.1090/S0002-9939-03-07055-2

Published electronically:
April 30, 2003

MathSciNet review:
1992860

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Abstract | References | Similar Articles | Additional Information

Abstract: We study a two-point free boundary problem for the curvature flow equation. By studying the corresponding nonlinear initial value problem, we obtain the existence and uniqueness of the forward self-similar solution of this problem. The corresponding curve is called the self-similar expanding curve. We also derive the asymptotic stability of this curve.

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Additional Information

**Hua-Huai Chern**

Affiliation:
Department of Computer and Information Sciences, National Taiwan Ocean University, 2, Pei-Ning Road, Keelung, Taiwan

Email:
felix@cs.ntou.edu.tw

**Jong-Shenq Guo**

Affiliation:
Department of Mathematics, National Taiwan Normal University, 88, S-4 Ting Chou Road, Taipei 117, Taiwan

Email:
jsguo@math.ntnu.edu.tw

**Chu-Pin Lo**

Affiliation:
Department of Applied Mathematics, Providence University, 200, Chung-Chi Road, Shalu, Taichung County 433, Taiwan

Email:
cplo@pu.edu.tw

DOI:
https://doi.org/10.1090/S0002-9939-03-07055-2

Received by editor(s):
May 16, 2002

Published electronically:
April 30, 2003

Communicated by:
David S. Tartakoff

Article copyright:
© Copyright 2003
American Mathematical Society