Study of Diophantine phenomena and exact asymptotic analysis of singular partial differential equations
| Project/Area Number |
20540172
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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 |
Basic analysis
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| Research Institution | Hiroshima University |
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Principal Investigator |
YOSHINO Masafumi Hiroshima University, 大学院・理学研究科, 教授 (00145658)
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| Co-Investigator(Kenkyū-buntansha) |
滝本 和広 広島大学, 大学院・理学研究科, 准教授 (00363044)
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| Co-Investigator(Renkei-kenkyūsha) |
TAKIMOTO Kazuhiro 広島大学, 大学院・理学研究科, 准教授 (00363044)
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| Project Period (FY) |
2008 – 2010
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| Project Status |
Completed (Fiscal Year 2010)
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| Budget Amount *help |
¥4,420,000 (Direct Cost: ¥3,400,000、Indirect Cost: ¥1,020,000)
Fiscal Year 2010: ¥1,430,000 (Direct Cost: ¥1,100,000、Indirect Cost: ¥330,000)
Fiscal Year 2009: ¥1,430,000 (Direct Cost: ¥1,100,000、Indirect Cost: ¥330,000)
Fiscal Year 2008: ¥1,560,000 (Direct Cost: ¥1,200,000、Indirect Cost: ¥360,000)
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| Keywords | 特異偏微分方程式 / ボレル総和法 / 小分母の問題 / ハミルトン系の非可積分性 / 漸近解析 / モーメント微分方程式 / Toeplitz作用素 / ベクトル場の標準形 / ハミルトン系 / 超級数 / 非可積分性 / 特異摂動 / 完全積分可能性 / 完全漸近解析 / Riemann-Hilbert分解 / パンルベ方程式 / 環境リスクモデル / 競争行列 / フックス型偏微分方程式 |
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| Research Abstract |
We showed analytical methods without the Diophantine condition in treating divergence of formal transformations in the normal form theory of a vector field. Our methods, based on asymptotic analysis, extend the so-called Borel-Laplace method, and give a real meaning to a divergent series in certain subdomain. Moreover, we give a meaning, by a Borel resummation method, to divergent first integrals of Hamiltonian systems , for which analytic non-integrability and smooth integrability occur similtaneously.
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Report
(4 results)
Research Products
(41 results)
