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 editorsFusco, Nicola; Julin, Vesa; Morini, Massimiliano

Journal or seriesJournal of Geometric Analysis

ISSN1050-6926

eISSN1559-002X

Publication year2022

Publication date05/01/2022

Volume32

Issue number2

Article number53

PublisherSpringer

Publication countryUnited States

Publication languageEnglish

DOIhttps://doi.org/10.1007/s12220-021-00806-x

Publication open accessNot 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.


Keywordspartial differential equations

Free keywordsforced mean curvature flow; large time behavior; stationary sets; critical sets


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Ministry reportingYes

Reporting Year2022

JUFO rating2


Last updated on 2024-03-04 at 19:06