2017 Fiscal Year Final Research Report
Mathematical analysis of superslow solution and anomalous diffusion
| Project/Area Number |
15K13455
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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 |
Foundations of mathematics/Applied mathematics
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| Research Institution | The University of Tokyo |
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Principal Investigator |
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| Project Period (FY) |
2015-04-01 – 2018-03-31
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| Keywords | 特異拡散 / 不均質媒質 / 非整数階偏微分方程式 / 凝集 / セシウムの特異拡散 |
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| Outline of Final Research Achievements |
In the case where a part of a plant is solved super-slowly and contaminants diffuse in hetrogeneous media such as soil, I mathematically analyzed. By the hetrogeneity, the profile in time and space does not indicate strong smoothing as the classical diffusion equation, and is known as anomalous diffusion. Within this project, I discuss fractional partial differential equations as models which can describe anomalous diffusion phenomena better, and have established the well-posedness of initial-boundary value problems and the uniqueness and the stability for various inverse problems such as the determination of coefficients in equations. Moreover I execute mathematical and numerical analyses for the anomalous diffusion of cesium and such results can interpret the real data well. I consider the superslow solution as a reciprocal process to the aggregation.
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| Free Research Field |
応用解析
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