Crystalline hexagonal curvature flow of networks: short-time, long-time and self-similar evolutions

We study the crystalline curvature flow of planar networks with a single hexagonal anisotropy. After proving the local existence of a classical solution for a rather large class of initial conditions, we classify the homothetically shrinking solutions having one bounded component. We also provide an...

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Bibliographic Details
Main Authors Bellettini, Giovanni, Kholmatov, Shokhrukh, Almuratov, Firdavsjon
Format Journal Article
LanguageEnglish
Published 27.01.2024
Subjects
Mathematics - Analysis of PDEs
Mathematics - Classical Analysis and ODEs
Mathematics - Differential Geometry
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Summary:We study the crystalline curvature flow of planar networks with a single hexagonal anisotropy. After proving the local existence of a classical solution for a rather large class of initial conditions, we classify the homothetically shrinking solutions having one bounded component. We also provide an example of network shrinking to a segment with multiplicity two.
DOI:10.48550/arxiv.2401.15358