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Convergence of Perturbed Allen Cahn Equations to Forced Mean Curvature Flow
Luca Mugnai and Matthias RögerAbstract
We study perturbations of the Allen--Cahn equation and prove the convergence to forced mean curvature flow in the sharp interface limit. We allow for perturbations that are square-integrable with respect to the diffuse surface area measure. We give a suitable generalized formulation for forced mean curvature flow and apply previous results for the Allen--Cahn action functional. Finally we discuss some applications.
- Received:
- 10.02.09
- Published:
- 05.03.09
- MSC Codes:
- 53C44, 35K55, 49Q15
- Keywords:
- Allen-Cahn equation, sharp interface limits, motion by mean curvature