Anchored spirals in the driven curvature flow approximation
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arXiv
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| Auteurs principaux: | , |
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| Format: | Preprint |
| Publié: |
2023
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| _version_ | 1866916125812457472 |
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| author | Li, Nan Scheel, Arnd |
| author_facet | Li, Nan Scheel, Arnd |
| contents | We study existence, asymptotics, and stability of spiral waves in a driven curvature approximation, supplemented with an anchoring condition on a circle of finite radius. We analyze the motion of curves written as graphs in polar coordinates, finding spiral waves as rigidly rotating shapes. The existence analysis reduces to a planar ODE and asymptotics are given through center manifold expansions. In the limit of a large core, we find rotation frequencies and corrections starting form a problem without curvature corrections. Finally, we demonstrate orbital stability of spiral waves by exploiting a comparison principle inherent to curvature driven flow. \end{abstract} |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2312_07809 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Anchored spirals in the driven curvature flow approximation Li, Nan Scheel, Arnd Pattern Formation and Solitons Analysis of PDEs We study existence, asymptotics, and stability of spiral waves in a driven curvature approximation, supplemented with an anchoring condition on a circle of finite radius. We analyze the motion of curves written as graphs in polar coordinates, finding spiral waves as rigidly rotating shapes. The existence analysis reduces to a planar ODE and asymptotics are given through center manifold expansions. In the limit of a large core, we find rotation frequencies and corrections starting form a problem without curvature corrections. Finally, we demonstrate orbital stability of spiral waves by exploiting a comparison principle inherent to curvature driven flow. \end{abstract} |
| title | Anchored spirals in the driven curvature flow approximation |
| topic | Pattern Formation and Solitons Analysis of PDEs |
| url | https://arxiv.org/abs/2312.07809 |