| Project/Area Number |
23340033
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| Research Category |
Grant-in-Aid for Scientific Research (B)
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| Allocation Type | Single-year Grants |
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| Section | 一般 |
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| Research Field |
Basic analysis
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| Research Institution | University of Tsukuba (2014)
Kagoshima University (2011-2013) |
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Principal Investigator |
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| Co-Investigator(Kenkyū-buntansha) |
MIYAJIMA Kimio 鹿児島大学, 大学院理工学研究科, 教授 (40107850)
KAKEHI Tomoyuki 岡山大学, 大学院自然科学研究科, 教授 (70231248)
ITOH Minoru 鹿児島大学, 大学院理工学研究科, 准教授 (60381141)
ONODERA Eiji 高知大学, 教育研究部自然科学系, 准教授 (70532357)
KAIZUKA Koichi 学習院大学, 理学部, 助教 (30737549)
小櫃 邦夫 鹿児島大学, 理工学研究科, 准教授 (00325763)
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| Research Collaborator |
YOSHINO Kazuhisa 筑波大学, 大学院数理物質科学研究科
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| Project Period (FY) |
2011-04-01 – 2015-03-31
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| Project Status |
Completed (Fiscal Year 2014)
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| Budget Amount *help |
¥18,200,000 (Direct Cost: ¥14,000,000、Indirect Cost: ¥4,200,000)
Fiscal Year 2014: ¥4,420,000 (Direct Cost: ¥3,400,000、Indirect Cost: ¥1,020,000)
Fiscal Year 2013: ¥4,420,000 (Direct Cost: ¥3,400,000、Indirect Cost: ¥1,020,000)
Fiscal Year 2012: ¥4,420,000 (Direct Cost: ¥3,400,000、Indirect Cost: ¥1,020,000)
Fiscal Year 2011: ¥4,940,000 (Direct Cost: ¥3,800,000、Indirect Cost: ¥1,140,000)
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| Keywords | 分散型写像流 / バーグマン変換 / 初期値問題 / テープリッツ作用素 / 幾何解析 / ゲルファント・シロフのクラス / ドブシーの局所化 / 適切性 / 擬微分作用素 / バーグマン型変換 / フーリエ積分作用素 / Berezin-Toeplitz 作用素 / 量子化 / 分散型偏微分方程式 / シュレーディンガー写像 |
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| Outline of Final Research Achievements |
We studied the initial value problem for dispersive flows of second, third and fourth orders from a point of view of geometric analysis and linear partial differential equations. We established the existence theorems for dispersive flows under the almost minimum restrictions on the geometric settings of the source and target manifolds. For example, we studied the second order equation which is called the Schroedinger map equation, whose solutions describe the flow from a closed Riemannian manifold to a compact almost Hermitian manifold, and succeeded in establishing the short-time existence theorem. This means that our geometric settings have no restriction as far as the description of the equation makes sense. In previous studies, the source manifold is supposed to be a circle (the one-dimensional torus) or an Euclidean space, and the target manifold is assumed to be a Kaehler manifold. For this reason, our results can be said to be big improvements.
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