Bibliographic Details
| Title: |
The evolution of immersed locally convex plane curves driven by anisotropic curvature flow |
| Authors: |
Wang Yaping, Wang Xiaoliu |
| Source: |
Advances in Nonlinear Analysis, Vol 12, Iss 1, Pp 117-131 (2022) |
| Publisher Information: |
De Gruyter, 2022. |
| Publication Year: |
2022 |
| Collection: |
LCC:Analysis |
| Subject Terms: |
curvature flow, anisotropy, long-time behaviour, singularity, 35b40, 35k15, 35k55, 53e10, – nonlinear analysis: perspectives and synergies, Analysis, QA299.6-433 |
| More Details: |
In this article, we study the evolution of immersed locally convex plane curves driven by anisotropic flow with inner normal velocity V=1αψ(x)καV=\frac{1}{\alpha }\psi \left(x){\kappa }^{\alpha } for α1\alpha \gt 1, where x∈[0,2mπ]x\in \left[0,2m\pi ] is the tangential angle at the point on evolving curves. For −1≤α1\alpha \gt 1, we show only type I singularity arises in the flow, and the rescaled flow has subsequential convergence, i.e. for any time sequence, there is a time subsequence along which the rescaled curvature of evolving curves converges to a limit function; furthermore, if the anisotropic function ψ\psi and the initial curve both have some symmetric structure, the subsequential convergence could be refined to be full-time convergence. |
| Document Type: |
article |
| File Description: |
electronic resource |
| Language: |
English |
| ISSN: |
2191-950X |
| Relation: |
https://doaj.org/toc/2191-950X |
| DOI: |
10.1515/anona-2022-0245 |
| Access URL: |
https://doaj.org/article/77eddf36c4274255bd6a583713d9b381 |
| Accession Number: |
edsdoj.77eddf36c4274255bd6a583713d9b381 |
| Database: |
Directory of Open Access Journals |
