Calculus of Variations and Geometric Measure Theory

N. Fusco - V. Julin - M. Morini

Stationary sets and asymptotic behavior of the mean curvature flow with forcing in the plane

created by morini on 16 Apr 2020
modified on 17 Apr 2020


Submitted Paper

Inserted: 16 apr 2020
Last Updated: 17 apr 2020

Year: 2020


We consider the flat flow solutions of the mean curvature equation with a forcing term in the plane. We prove that for every constant forcing term the stationary sets are given by a finite union of disks with equal radii and disjoint closures. On the other hand for every bounded forcing term tangent disks are never stationary. Finally in the case of an asymptotically constant forcing term we show that the only possible long time limit sets are given by disjoint unions of disks with equal radii and possibly tangent.