Elastic flow of curves with partial free boundary
Fuente:
arXiv
Gespeichert in:
| 1. Verfasser: | |
|---|---|
| Format: | Preprint |
| Veröffentlicht: |
2023
|
| Schlagworte: | |
| Online-Zugang: | |
| Tags: |
Tag hinzufügen
Keine Tags, Fügen Sie den ersten Tag hinzu!
|
| _version_ | 1866913402935312384 |
|---|---|
| author | Diana, Antonia |
| author_facet | Diana, Antonia |
| contents | We consider a curve with boundary points free to move on a line in $\mathbb R^2$, which evolves by the $L^2$--gradient flow of the elastic energy, that is a linear combination of the Willmore and the length functional. For such planar evolution problem we study the short and long--time existence.
Once we establish under which boundary conditions the PDE's system is well--posed (in our case the Navier boundary conditions), employing the Solonnikov theory for linear parabolic systems in Hölder space, we show that there exists a unique flow in a maximal time interval $[0,T)$. Then, using energy methods we prove that the maximal time is actually $T= + \infty$. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2310_14738 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Elastic flow of curves with partial free boundary Diana, Antonia Analysis of PDEs 53E40, 35G31, 35A01 We consider a curve with boundary points free to move on a line in $\mathbb R^2$, which evolves by the $L^2$--gradient flow of the elastic energy, that is a linear combination of the Willmore and the length functional. For such planar evolution problem we study the short and long--time existence. Once we establish under which boundary conditions the PDE's system is well--posed (in our case the Navier boundary conditions), employing the Solonnikov theory for linear parabolic systems in Hölder space, we show that there exists a unique flow in a maximal time interval $[0,T)$. Then, using energy methods we prove that the maximal time is actually $T= + \infty$. |
| title | Elastic flow of curves with partial free boundary |
| topic | Analysis of PDEs 53E40, 35G31, 35A01 |
| url | https://arxiv.org/abs/2310.14738 |