2023 Fiscal Year Final Research Report
Homogenization in Anomalous Diffusion Phenomena and its Applications to Inverse Problems
| Project/Area Number |
21K20333
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| Research Category |
Grant-in-Aid for Research Activity Start-up
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| Allocation Type | Multi-year Fund |
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| Review Section |
0201:Algebra, geometry, analysis, applied mathematics,and related fields
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| Research Institution | Takushoku University |
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Principal Investigator |
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| Project Period (FY) |
2021-08-30 – 2024-03-31
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| Keywords | 逆問題 / 数理モデル / 異常拡散現象 / 非整数階拡散方程式 / 均質化法 |
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| Outline of Final Research Achievements |
In soil contamination, the diffusion of contaminants in soil is different from classical diffusion and is called anomalous diffusion. We focused on time-fractional diffusion equations which describe anomalous diffusion, and studied the homogenization for the time-fractional diffusion equations and its applications to inverse problems.
In particular, we proposed new inverse coefficient problems between a periodic structure and a homogenized one, and succeeded in deriving the uniqueness and the stability in the inverse problems between these different structures by using the results of the homogenization and others.
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| Free Research Field |
偏微分方程式
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| Academic Significance and Societal Importance of the Research Achievements |
学術的意義：時間非整数階拡散方程式に対する均質化法の数学的に厳密な議論による結果は先駆的研究のひとつである．また，本研究で新たに提案した周期的な構造と均質化された構造との異なる構造間の逆問題とその数学解析の結果は，今まで存在せず，学術的に独創性がある．
社会的意義：本研究は土壌汚染の問題に応用可能であり，数学的に厳密な理論的保証を与えるものである．また，土壌汚染における汚染の予測や汚染源の除去など現実の問題解決に効果的な指針を示すことが期待できる．
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