Luca Mugnai, Matthias Röger
Published 2009-02-11Version 1
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.
Convergence to equilibrium of gradient flows defined on planar curves
On the convergence of statistical solutions of the 3D Navier-Stokes-$α$ model as $α$ vanishes
On convergence of solutions to equilibria for fully nonlinear parabolic problems with nonlinear boundary conditions
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