Garcke, Harald and Matioc, Bogdan-Vasile (2021) On a degenerate parabolic system describing the mean curvature flow of rotationally symmetric closed surfaces. JOURNAL OF EVOLUTION EQUATIONS, 21. pp. 201-224. ISSN 1424-3199, 1424-3202
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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.
| Item Type: | Article |
|---|---|
| Uncontrolled Keywords: | REGULARITY; SINGULARITIES; ANALYTICITY; INTERFACE; Mean curvature flow; Degenerate parabolic equation; Maximal regularity; Parabolic smoothing |
| Subjects: | 500 Science > 510 Mathematics |
| Divisions: | Mathematics > Prof. Dr. Harald Garcke |
| Depositing User: | Petra Gürster |
| Date Deposited: | 08 Apr 2021 06:00 |
| Last Modified: | 08 Apr 2021 06:00 |
| URI: | https://pred.uni-regensburg.de/id/eprint/44779 |
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