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FRACTIONAL TIME DIFFERENTIAL EQUATIONS AS A SINGULAR LIMIT OF THE KOBAYASHI-WARREN-CARTER SYSTEM
| Title: | FRACTIONAL TIME DIFFERENTIAL EQUATIONS AS A SINGULAR LIMIT OF THE KOBAYASHI-WARREN-CARTER SYSTEM |
| Authors: | GIGA, YOSHIKAZU Browse this author →KAKEN DB | | KUBO, AYATO Browse this author | | KURODA, HIROTOSHI Browse this author →KAKEN DB | | OKAMOTO, JUN Browse this author | | SAKAKIBARA, KOYA Browse this author | | UESAKA, MASAAKI Browse this author |
| Issue Date: | 29-Jun-2023 |
| Publisher: | Department of Mathematics, Hokkaido University |
| Journal Title: | Hokkaido University Preprint Series in Mathematics |
| Volume: | 1152 |
| Start Page: | 1 |
| End Page: | 24 |
| Abstract: | This paper is concerned with a singular limit of the Kobayashi-Warren-Carter system, a phase field system modelling the evolutions of structures of grains. Under a suitable scaling, the limit system is formally derived when the interface thickness parameter tends to zero. Different from many other problems, it turns out that the limit system is a system involving fractional time derivatives, although the original system is a simple gradient flow. A rigorous derivation is given when the problem is reduced to a gradient flow of a single-well Modica{Mortola functional in a one-dimensional setting. |
| Type: | bulletin (article) |
| URI: | http://hdl.handle.net/2115/90095 |
| 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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