On a degenerate parabolic system describing the mean curvature flow of rotationally symmetric closed surfaces
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arXiv
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| Main Authors: | , |
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| Format: | Preprint |
| Published: |
2019
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| _version_ | 1866910421875687424 |
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| author | Garcke, Harald Matioc, Bogdan-Vasile |
| author_facet | Garcke, Harald Matioc, Bogdan-Vasile |
| contents | We show that the mean curvature flow for a closed and rotationally symmetric surface can be formulated as an evolution problem consisting of an evolution equation for the square of the function whose graph is rotated and two ODEs describing the evolution of the points of the evolving surface that lie on the rotation axis. For the fully nonlinear and degenerate parabolic problem we establish the well-posedness property in the setting of classical solutions. Besides we prove that the problem features the effect of parabolic smoothing. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_1905_09675 |
| institution | arXiv |
| publishDate | 2019 |
| record_format | arxiv |
| spellingShingle | On a degenerate parabolic system describing the mean curvature flow of rotationally symmetric closed surfaces Garcke, Harald Matioc, Bogdan-Vasile Analysis of PDEs 35K55, 53C44, 35R35, 35K93 We show that the mean curvature flow for a closed and rotationally symmetric surface can be formulated as an evolution problem consisting of an evolution equation for the square of the function whose graph is rotated and two ODEs describing the evolution of the points of the evolving surface that lie on the rotation axis. For the fully nonlinear and degenerate parabolic problem we establish the well-posedness property in the setting of classical solutions. Besides we prove that the problem features the effect of parabolic smoothing. |
| title | On a degenerate parabolic system describing the mean curvature flow of rotationally symmetric closed surfaces |
| topic | Analysis of PDEs 35K55, 53C44, 35R35, 35K93 |
| url | https://arxiv.org/abs/1905.09675 |