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.

Stationary Sets and Asymptotic Behavior of the Mean Curvature Flow with Forcing in the Plane / Fusco, N.; Julin, V.; Morini, M.. - In: THE JOURNAL OF GEOMETRIC ANALYSIS. - ISSN 1050-6926. - 32:2(2022). [10.1007/s12220-021-00806-x]

Stationary Sets and Asymptotic Behavior of the Mean Curvature Flow with Forcing in the Plane

Fusco N.;Morini M.
2022

Abstract

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.
Stationary Sets and Asymptotic Behavior of the Mean Curvature Flow with Forcing in the Plane / Fusco, N.; Julin, V.; Morini, M.. - In: THE JOURNAL OF GEOMETRIC ANALYSIS. - ISSN 1050-6926. - 32:2(2022). [10.1007/s12220-021-00806-x]
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Utilizza questo identificativo per citare o creare un link a questo documento: http://hdl.handle.net/11381/2914297
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