A1 Journal article (refereed)
Stationary Sets and Asymptotic Behavior of the Mean Curvature Flow with Forcing in the Plane (2022)

Fusco, N., Julin, V., & Morini, M. (2022). Stationary Sets and Asymptotic Behavior of the Mean Curvature Flow with Forcing in the Plane. Journal of Geometric Analysis, 32(2), Article 53. https://doi.org/10.1007/s12220-021-00806-x

JYU authors or editors

Publication details

All authors or editors: Fusco, Nicola; Julin, Vesa; Morini, Massimiliano

Journal or series: Journal of Geometric Analysis

ISSN: 1050-6926

eISSN: 1559-002X

Publication year: 2022

Publication date: 05/01/2022

Volume: 32

Issue number: 2

Article number: 53

Publisher: Springer

Publication country: United States

Publication language: English

DOI: https://doi.org/10.1007/s12220-021-00806-x

Publication open access: Not open

Publication channel open access: 

Publication is parallel published (JYX): https://jyx.jyu.fi/handle/123456789/85378

Web address of parallel published publication (pre-print): https://arxiv.org/abs/2004.07734

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.

Keywords: partial differential equations

Free keywords: forced mean curvature flow; large time behavior; stationary sets; critical sets

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Related projects

Ministry reporting: Yes

VIRTA submission year: 2022

JUFO rating: 2