Stationary Sets and Asymptotic Behavior of the Mean Curvature Flow with Forcing in the Plane
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.
Main Authors
Format
Articles
Research article
Published
2022
Series
Subjects
Publication in research information system
Publisher
Springer
The permanent address of the publication
https://urn.fi/URN:NBN:fi:jyu-202302071658Use this for linking
Review status
Peer reviewed
ISSN
1050-6926
DOI
https://doi.org/10.1007/s12220-021-00806-x
Language
English
Published in
Journal of Geometric Analysis
Citation
- 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
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Funder(s)
Research Council of Finland
Funding program(s)
Research costs of Academy Research Fellow, AoF
Akatemiatutkijan tutkimuskulut, SA
Additional information about funding
The research of N.F. has been funded by PRIN Project 2015PA5MP7. The research of V.J. was supported by the Academy of Finland grant 314227. N.F. and M.M. are members of Gruppo Nazionale per l’Analisi Matematica, la Probabilità e le loro Applicazioni (GNAMPA) of INdAM.
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