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A convergence result for a minimizing movement scheme for mean curvature flow with prescribed contact angle in a curved domain
| Title: | A convergence result for a minimizing movement scheme for mean curvature flow with prescribed contact angle in a curved domain |
| Authors: | Eto, Tokuhiro Browse this author | | Giga, Yoshikazu Browse this author →KAKEN DB |
| Issue Date: | 27-Feb-2024 |
| Publisher: | Department of Mathematics, Hokkaido University |
| Journal Title: | Hokkaido University Preprint Series in Mathematics |
| Volume: | 1155 |
| Start Page: | 1 |
| End Page: | 31 |
| Abstract: | We consider a minimizing movement scheme of Chambolle type for the mean curvature flow equation with prescribed contact angle condition in a smooth bounded domain in Rd (d 2). We prove that an approximate solution constructed by the proposed scheme converges to the level-set mean curvature flow with prescribed contact angle provided that the domain is convex and that the contact angle is away from zero under some control of derivatives of given prescribed angle. We actually prove that an auxiliary function corresponding to the scheme uniformly converges to a unique viscosity solution to the level-set equation with an oblique derivative boundary condition corresponding to the prescribed boundary condition. |
| Type: | bulletin (article) |
| URI: | http://hdl.handle.net/2115/91201 |
| 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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