IUMJ

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

Authors: Luca Mugnai and Matthias Roeger

Issue: Volume 60 (2011), Issue 1, 41-76

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.