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

Part of: Parabolic equations and systems Global differential geometry

Published online by Cambridge University Press:  07 February 2011

XIAOLIU WANG  and
WEIFENG WO
XIAOLIU WANG*
Affiliation:
Department of Mathematics, Southeast University, No. 2 Sipailou, Nanjing 210096, PR China (email: xlwang.seu@gmail.com)
WEIFENG WO
Affiliation:
Department of Mathematics, The Chinese University of Hong Kong, Shatin, Hong Kong (email: weifengwo@gmail.com)
*
✉For correspondence; e-mail: xlwang.seu@gmail.com
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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.

Keywords

curvature flowasymptotic behaviorstability

MSC classification

Secondary: 35K55: Nonlinear parabolic equations 35K15: Initial value problems for second-order parabolic equations 53C44: Geometric evolution equations (mean curvature flow, Ricci flow, etc.)

Information

Type
Research Article
Information
Bulletin of the Australian Mathematical Society , Volume 83 , Issue 2 , April 2011 , pp. 177 - 188
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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