Time-fractional Allen-Cahn equations versus powers of the mean curvature
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arXiv
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| Main Authors: | , , |
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| Format: | Preprint |
| Published: |
2024
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| _version_ | 1866911817761030144 |
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| author | Dipierro, Serena Novaga, Matteo Valdinoci, Enrico |
| author_facet | Dipierro, Serena Novaga, Matteo Valdinoci, Enrico |
| contents | We show by a formal asymptotic expansion that level sets of solutions of a time-fractional Allen-Cahn equation evolve by a geometric flow whose normal velocity is a positive power of the mean curvature.
This connection is quite intriguing, since the original equation is nonlocal and the evolution of its solutions depends on all previous states, but the associated geometric flow is of purely local type, with no memory effect involved. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2402_05250 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Time-fractional Allen-Cahn equations versus powers of the mean curvature Dipierro, Serena Novaga, Matteo Valdinoci, Enrico Analysis of PDEs We show by a formal asymptotic expansion that level sets of solutions of a time-fractional Allen-Cahn equation evolve by a geometric flow whose normal velocity is a positive power of the mean curvature. This connection is quite intriguing, since the original equation is nonlocal and the evolution of its solutions depends on all previous states, but the associated geometric flow is of purely local type, with no memory effect involved. |
| title | Time-fractional Allen-Cahn equations versus powers of the mean curvature |
| topic | Analysis of PDEs |
| url | https://arxiv.org/abs/2402.05250 |