| Project/Area Number |
23654030
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| Research Category |
Grant-in-Aid for Challenging Exploratory Research
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| Allocation Type | Multi-year Fund |
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| Research Field |
General mathematics (including Probability theory/Statistical mathematics)
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| Research Institution | The University of Tokyo |
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Principal Investigator |
YAMAMOTO Masahiro 東京大学, 数理(科)学研究科(研究院), 教授 (50182647)
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| Co-Investigator(Kenkyū-buntansha) |
HATANO Yuko 筑波大学, システム情報工学科, 准教授 (60323276)
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| Project Period (FY) |
2011 – 2013
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| Project Status |
Completed (Fiscal Year 2013)
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| Budget Amount *help |
¥3,510,000 (Direct Cost: ¥2,700,000、Indirect Cost: ¥810,000)
Fiscal Year 2013: ¥1,170,000 (Direct Cost: ¥900,000、Indirect Cost: ¥270,000)
Fiscal Year 2012: ¥1,040,000 (Direct Cost: ¥800,000、Indirect Cost: ¥240,000)
Fiscal Year 2011: ¥1,300,000 (Direct Cost: ¥1,000,000、Indirect Cost: ¥300,000)
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| Keywords | 不均質媒質 / 汚染物質拡散 / 非整数階拡散方程式 / 連続時間ランダムウォーク / 非整数階微分方程式 / 汚染物質の拡散 / 異常拡散 / マルチスケール / 逆問題 / ミクロモデル / マクロモデル / マルチスケールモデル |
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| Research Abstract |
It is known that the classical advection-diffusion equation is not an adequate model for diffusion processs of contaminants in heterogenous media such as soil.
For real methods for keeping the environmental safety, we have studied the con-tinuous-time random walk as microscopic model and the fractional diffusion quation as macroscopic model. Our achievements are as follows: (1) We relate both models: the continuous-time random walk and the fractional diffusion quation, and derive other from another, and we propose better models on the basis of such studies. (2) Mathematical analysis such as the unique existence of solution and the asymptotic behavior. (3) Mathematical analysis and numerical methods for inverse contamination source
problems.
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