Search

MiS Preprint Repository

Delve into the future of research at MiS with our preprint repository. Our scientists are making groundbreaking discoveries and sharing their latest findings before they are published. Explore repository to stay up-to-date on the newest developments and breakthroughs.

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:
Feb 10, 2009
Published:
Mar 5, 2009
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