Advances in Differential Equations
- Adv. Differential Equations
- Volume 12, Number 5 (2007), 481-514.
Optimal rate of convergence to the motion by mean curvature with a driving force
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.
Adv. Differential Equations Volume 12, Number 5 (2007), 481-514.
First available in Project Euclid: 29 April 2013
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Ishii, Katsuyuki. Optimal rate of convergence to the motion by mean curvature with a driving force. Adv. Differential Equations 12 (2007), no. 5, 481--514.https://projecteuclid.org/euclid.ade/1367241434