Analysis for multi-scale models describing nonlinear phenomena in porous media
| Project/Area Number |
15K04969
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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 |
Mathematical analysis
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| Research Institution | Japan Women's University |
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Principal Investigator |
Aiki Toyohiko 日本女子大学, 理学部, 教授 (90231745)
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| Co-Investigator(Kenkyū-buntansha) |
熊崎 耕太 苫小牧工業高等専門学校, 創造工学科, 准教授 (30634563)
村瀬 勇介 名城大学, 理工学部, 助教 (80546771)
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| Project Period (FY) |
2015-04-01 – 2018-03-31
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| Project Status |
Completed (Fiscal Year 2017)
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| Budget Amount *help |
¥4,680,000 (Direct Cost: ¥3,600,000、Indirect Cost: ¥1,080,000)
Fiscal Year 2017: ¥1,430,000 (Direct Cost: ¥1,100,000、Indirect Cost: ¥330,000)
Fiscal Year 2016: ¥1,430,000 (Direct Cost: ¥1,100,000、Indirect Cost: ¥330,000)
Fiscal Year 2015: ¥1,820,000 (Direct Cost: ¥1,400,000、Indirect Cost: ¥420,000)
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| Keywords | 自由境界問題 / マルチスケールモデル / マルチスケール / 多孔質媒体 / コンクリート中性化 / ヒステリシス / 制御問題 / 周期解 |
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| Outline of Final Research Achievements |
We have established global existence of a solution to the free boundary problem describing a relationship between the degree of saturation and relative humidity in porous media. By applying this result, we have proved convergence to a steady solution, existence of a periodic solution, and a continuity of solutions of the free boundary problem with varying boundary data by some parameter. Furthermore, we can get a solution, locally in time, of a multi-scale model corresponding to mass conservation law of water in porous media.
Also, we generalized the model describing the relationship by the ordinary differential equation and proved existence of a solution to an optimal control problem. Moreover, we have proposed a new free boundary problem for swelling phenomena in porous media and obtained its local solution in time.
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Report
(4 results)
Research Products
(49 results)
