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We have decided to discontinue the publication of preprints on our preprint server as of 1 March 2024. The publication culture within mathematics has changed so much due to the rise of repositories such as ArXiV (www.arxiv.org) that we are encouraging all institute members to make their preprints available there. An institute's repository in its previous form is, therefore, unnecessary. The preprints published to date will remain available here, but we will not add any new preprints here.

MiS Preprint
13/2009

Convergence of Perturbed Allen Cahn Equations to Forced Mean Curvature Flow

Luca Mugnai and Matthias Röger

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.

Received:
10.02.09
Published:
05.03.09
MSC Codes:
53C44, 35K55, 49Q15
Keywords:
Allen-Cahn equation, sharp interface limits, motion by mean curvature

Related publications

inJournal
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