2010 Fiscal Year Final Research Report
Studies on approximation, regularity and singularity for mean curvature flow
| Project/Area Number |
20540117
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| Research Category |
Grant-in-Aid for Scientific Research (C)
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| Allocation Type | Single-year Grants |
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| Section | 一般 |
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| Research Field |
General mathematics (including Probability theory/Statistical mathematics)
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| Research Institution | Kobe University |
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Principal Investigator |
ISHII Katsuyuki Kobe University, 海事科学研究科, 准教授 (40232227)
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| Co-Investigator(Kenkyū-buntansha) |
MARUO Kenji 神戸大学, 大学院・海事科学研究科, 教授 (90028225)
NAITO Yuki 愛媛大学, 大学院・理工学研究科, 教授 (10231458)
KUWAMURA Masataka 神戸大学, 大学院・人間環境発達学研究科, 准教授 (30270333)
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| Co-Investigator(Renkei-kenkyūsha) |
TAKAHASHI Futoshi 大阪市立大学, 大学院・理学研究科, 教授 (10374901)
ISHIWATA Tetsuya 芝浦工業大学, システム理工学部, 准教授 (50334917)
OHMUNA Masaki 徳島大学, ソシオ・アーツ・サイエンス研究部, 准教授 (90304500)
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| Project Period (FY) |
2008 – 2010
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| Keywords | 非線形偏微分方程式 / 平均曲率流 / 粘性解 / 自由境界 / 数理ファイナンス |
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| Research Abstract |
We consider an approximation scheme for anisotropic curvature flow, arising from the image processing., and prove the convergence of this scheme. We also study the parabolic free boundary problems arising from mathematical finance. We introduce a time-discrete scheme for a parabolic variational inequality and obtain the convergences of approximate solutions and approximate free boundaries. We also prove the existence and uniqueness of solutions and of free boundary for an investment problem.
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