A dynamic approach to heterogeneous elastic wires
Fuente:
arXiv
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| Autores principales: | , , |
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| Formato: | Preprint |
| Publicado: |
2022
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| Acceso en línea: | |
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| _version_ | 1866916125289218048 |
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| author | Dall'Acqua, Anna Langer, Leonie Rupp, Fabian |
| author_facet | Dall'Acqua, Anna Langer, Leonie Rupp, Fabian |
| contents | We consider closed planar curves with fixed length and arbitrary winding number whose elastic energy depends on an additional density variable and a spontaneous curvature. Working with the inclination angle, the associated $L^2$-gradient flow is a nonlocal quasilinear coupled parabolic system of second order. We show local well-posedness, global existence of solutions, and full convergence of the flow for initial data in a weak regularity class. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2205_06587 |
| institution | arXiv |
| publishDate | 2022 |
| record_format | arxiv |
| spellingShingle | A dynamic approach to heterogeneous elastic wires Dall'Acqua, Anna Langer, Leonie Rupp, Fabian Analysis of PDEs Differential Geometry 35K45 (primary), 53E10 (secondary) We consider closed planar curves with fixed length and arbitrary winding number whose elastic energy depends on an additional density variable and a spontaneous curvature. Working with the inclination angle, the associated $L^2$-gradient flow is a nonlocal quasilinear coupled parabolic system of second order. We show local well-posedness, global existence of solutions, and full convergence of the flow for initial data in a weak regularity class. |
| title | A dynamic approach to heterogeneous elastic wires |
| topic | Analysis of PDEs Differential Geometry 35K45 (primary), 53E10 (secondary) |
| url | https://arxiv.org/abs/2205.06587 |