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

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

2009-02-11

arxiv.org/abs/0902.1816v1

Mathematics

Analysis of PDEs

23 pages

Scientific paper

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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