Convergence of Perturbed Allen–cahn Equations to Forced Mean Curvature Flow
نویسندگان
چکیده
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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