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| Main Author: | |
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| Format: | Preprint |
| Published: |
2024
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2408.03823 |
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| _version_ | 1866913746447761408 |
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| author | Langer, Leonie |
| author_facet | Langer, Leonie |
| contents | We derive an $H^{-1}$-gradient flow of the elastic energy which preserves the enclosed area of evolving planar curves. For this new sixth-order evolution equation, we prove a global existence result. Additionally, by penalizing the length, we show convergence to an area constrained critical point of the elastic energy. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2408_03823 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Dynamics of Elastic Wires: Preserving Area without Nonlocality Langer, Leonie Analysis of PDEs 53E40 (primary), 35K30, 35B40 (secondary) We derive an $H^{-1}$-gradient flow of the elastic energy which preserves the enclosed area of evolving planar curves. For this new sixth-order evolution equation, we prove a global existence result. Additionally, by penalizing the length, we show convergence to an area constrained critical point of the elastic energy. |
| title | Dynamics of Elastic Wires: Preserving Area without Nonlocality |
| topic | Analysis of PDEs 53E40 (primary), 35K30, 35B40 (secondary) |
| url | https://arxiv.org/abs/2408.03823 |