## Advances in Differential Equations

### Optimal rate of convergence to the motion by mean curvature with a driving force

Katsuyuki Ishii

#### 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.

#### Article information

Source
Adv. Differential Equations, Volume 12, Number 5 (2007), 481-514.

Dates
First available in Project Euclid: 29 April 2013

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