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ON THE STABILITY OF STATIONARY LINE AND GRIM REAPER IN PLANAR CURVATURE FLOW

Published online by Cambridge University Press:  07 February 2011

XIAOLIU WANG*
Affiliation:
Department of Mathematics, Southeast University, No. 2 Sipailou, Nanjing 210096, PR China (email: [email protected])
WEIFENG WO
Affiliation:
Department of Mathematics, The Chinese University of Hong Kong, Shatin, Hong Kong (email: [email protected])
*
For correspondence; e-mail: [email protected]
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Abstract

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The asymptotic stability of two types of invariant solutions under a curvature flow in the whole plane is studied. First, by extending the work of others, we prove that the stationary line with nonzero slope will attract the graphical curves which surround it. Then a similar property is obtained for the grim reaper.

Type
Research Article
Copyright
Copyright © Australian Mathematical Publishing Association Inc. 2011

Footnotes

This work is supported by the Grant for New PhD Teacher Program of Southeast University.

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