A study of solutions of systems of higher order partial differential equations by algebraic analysis methods and formula manipulation methods
| Project/Area Number |
26400110
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| Research Category |
Grant-in-Aid for Scientific Research (C)
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| Allocation Type | Multi-year Fund |
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| Section | 一般 |
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| Research Field |
Basic analysis
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| Research Institution | The University of Tokyo |
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Principal Investigator |
Kataoka Kiyoomi 東京大学, 大学院数理科学研究科, 名誉教授 (60107688)
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| Project Period (FY) |
2014-04-01 – 2018-03-31
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| Project Status |
Completed (Fiscal Year 2017)
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| Budget Amount *help |
¥3,120,000 (Direct Cost: ¥2,400,000、Indirect Cost: ¥720,000)
Fiscal Year 2016: ¥650,000 (Direct Cost: ¥500,000、Indirect Cost: ¥150,000)
Fiscal Year 2015: ¥910,000 (Direct Cost: ¥700,000、Indirect Cost: ¥210,000)
Fiscal Year 2014: ¥1,560,000 (Direct Cost: ¥1,200,000、Indirect Cost: ¥360,000)
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| Keywords | 解析関数 / 偏微分方程式系 / 初期値・境界値混合問題 / D-加群 / 佐藤超関数 / 層のマイクロ台 / 一般化固有関数 / 蔵本モデル / 蔵本予想 / 共鳴現象 / 非線形発展方程式 / 一般化固有値 / 解析性 / 分布関数 / ヒルベルト空間 / レゾルベント / ガウス分布 / 共鳴極 / 漸近展開 / 初期値境界値混合問題 / 超局所解析 / 回折現象 / Lopatinskii条件 / マイクロ台 / 円の族を含む曲面 / ５階偏微分方程式系 / 非線形偏微分方程式系 / 数式処理 / 境界値問題 / 代数解析 |
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| Outline of Final Research Achievements |
Concerning systems of linear analytic partial differential equations, we succeeded in giving coordinate-free formulations of the initial-boundary value mixed problems for D_X modules. At the same time we obtained a key theorem on the estimate of micro-supports of some holomorphic solution sheaf complexes in the sense of M.Kashiwara-P.Schapira, which is an essential tool clarifying the propagation of micro-analyticity of Sato hyperfunction solutions along the boundary. Concerning non-linear differential equations, we succeeded in clarifying the generalized eigenfunction expansions due to Hayato Chiba's theory on Kuramoto's weakly coupled many oscillators model on a circle for resonance phenomena. We found some essential error in Chiba's theory and gave a correct formulation and a proof.
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Report
(5 results)
Research Products
(11 results)
