Convergence of perturbed Allen-Cahn equations to forced mean curvature flow
Abstract
Description
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.
23 pages
23 pages