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arXiv · 0902.1816

Convergence of perturbed Allen-Cahn equations to forced mean curvature flow

Luca Mugnai·Matthias Röger
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Abstract

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.

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Luca Mugnai, Matthias Röger. 2009-02-11. Convergence of perturbed Allen-Cahn equations to forced mean curvature flow. https://arxiv.org/abs/0902.1816

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