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MiS Preprint

Convergence of Perturbed Allen Cahn Equations to Forced Mean Curvature Flow

Luca Mugnai and Matthias Röger


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.

Feb 10, 2009
Mar 5, 2009
MSC Codes:
53C44, 35K55, 49Q15
Allen-Cahn equation, sharp interface limits, motion by mean curvature

Related publications

2011 Repository Open Access
Luca Mugnai and Matthias Röger

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

In: Indiana University mathematics journal, 60 (2011) 1, pp. 41-75