6533b871fe1ef96bd12d1132

RESEARCH PRODUCT

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

Nicola FuscoVesa JulinMassimiliano Morini

subject

osittaisdifferentiaaliyhtälötMathematics - Analysis of PDEsforced mean curvature flowFOS: Mathematicsstationary setscritical setsGeometry and TopologyAstrophysics::Earth and Planetary Astrophysicslarge time behaviorAnalysis of PDEs (math.AP)

description

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. peerReviewed

yearjournalcountryeditionlanguage
2020-04-16
http://arxiv.org/abs/2004.07734