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Hokkaido University Preprint Series in Mathematics >
A level-set method for a mean curvature flow with a prescribed boundary
| Title: | A level-set method for a mean curvature flow with a prescribed boundary |
| Authors: | Bian, Xing zhi Browse this author | | Giga, Yoshikazu Browse this author →KAKEN DB | | Mitake, Hiroyoshi Browse this author →KAKEN DB |
| Keywords: | mean curvature flow | | level-set method | | Dirichlet problem | | obstacle problem |
| Issue Date: | 29-Jun-2023 |
| Publisher: | Department of Mathematics, Hokkaido University |
| Journal Title: | Hokkaido University Preprint Series in Mathematics |
| Volume: | 1151 |
| Start Page: | 1 |
| End Page: | 26 |
| Abstract: | We propose a level-set method for a mean curvature flow whose boundary is prescribed by interpreting the boundary as an obstacle. Since the corresponding obstacle problem is globally solvable, our method gives a global-in-time level-set mean curvature flow under a prescribed boundary with no restriction of the profile of an initial hypersurface. We show that our solution agrees with a classical mean curvature flow under the Dirichlet condition. We moreover prove that our solution agrees with a level-set flow under the Dirichlet condition constructed by P. Sternberg and W. P. Ziemer (1994), where the initial hypersurface is contained in a strictly mean-convex domain and the prescribed boundary is on the boundary of the domain. |
| Type: | bulletin (article) |
| URI: | http://hdl.handle.net/2115/90094 |
| Appears in Collections: | 理学院・理学研究院 (Graduate School of Science / Faculty of Science) > Hokkaido University Preprint Series in Mathematics
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Submitter: 数学紀要登録作業用
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