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2007 Optimal rate of convergence to the motion by mean curvature with a driving force
Katsuyuki Ishii
Adv. Differential Equations 12(5): 481-514 (2007).

Abstract

We consider a singularly perturbed parabolic problem with a small parameter $ \varepsilon>0 $. This problem can be regarded as an approximation of the motion of a hypersurface by its mean curvature with a driving force. In this paper we derive a rate of convergence of an order $ \varepsilon^2 $ for the motion of a smooth and compact hypersurface by its mean curvature with a driving force. We also consider the special case of a circle evolving by its curvature and show that our rate is optimal.

Citation

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Katsuyuki Ishii. "Optimal rate of convergence to the motion by mean curvature with a driving force." Adv. Differential Equations 12 (5) 481 - 514, 2007.

Information

Published: 2007
First available in Project Euclid: 29 April 2013

zbMATH: 1171.35009
MathSciNet: MR2321563

Subjects:
Primary: 35K55
Secondary: 35B25, 53C44

Rights: Copyright © 2007 Khayyam Publishing, Inc.

JOURNAL ARTICLE
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Vol.12 • No. 5 • 2007
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