Mathematical analysis for concrete carbonation applying the regularity of a solution of quasi-linear parabolic equations
| Project/Area Number |
16K17636
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| Research Category |
Grant-in-Aid for Young Scientists (B)
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| Allocation Type | Multi-year Fund |
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| Research Field |
Mathematical analysis
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| Research Institution | Nagasaki University (2018-2020)
Tomakomai National College of Technology (2016-2017) |
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Principal Investigator |
KUMAZAKI Kota 長崎大学, 教育学部, 准教授 (30634563)
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| Project Period (FY) |
2016-04-01 – 2021-03-31
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| Project Status |
Completed (Fiscal Year 2020)
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| Budget Amount *help |
¥3,770,000 (Direct Cost: ¥2,900,000、Indirect Cost: ¥870,000)
Fiscal Year 2019: ¥780,000 (Direct Cost: ¥600,000、Indirect Cost: ¥180,000)
Fiscal Year 2018: ¥780,000 (Direct Cost: ¥600,000、Indirect Cost: ¥180,000)
Fiscal Year 2017: ¥910,000 (Direct Cost: ¥700,000、Indirect Cost: ¥210,000)
Fiscal Year 2016: ¥1,300,000 (Direct Cost: ¥1,000,000、Indirect Cost: ¥300,000)
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| Keywords | 中性化現象 / 水分の輸送モデル / 准線形放物型方程式 / 自由境界問題 / 解の存在と一意性 / 数学解析 / 非線形現象 / 数理モデル / 準線形放物型方程式 |
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| Outline of Final Research Achievements |
In this study, we derived a new transport model for moisture which combined a quasi-linear parabolic equation for the relative humidity distributed the whole material and a free boundary problem for the water saturation in microscopic pores. For this model, we succeeded in showing and the existence of a locally-in-time solution and a global-in-time solution, and the continuous dependence between the relative humidity and saturation.
Also, we proposed a transport model for carbon dioxide that takes into account the mutual changes between the atmosphere and water and showed the existence of a globally-in-time solution under a realistic boundary condition. Based on these results, we consider a mathematical model describing carbonation process consists of the above two transport models and succeeded in showing the existence of a locally-in-time solution by making a smooth approximation of the external force of the quasi-linear parabolic equation.
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| Academic Significance and Societal Importance of the Research Achievements |
中性化現象は、建造物の持続性を損なう原因として、近年、関連する物質の輸送モデルが提案され、数値的な解析が進められているが、その妥当性は検証されていない。本研究では、中性化現象の中心である水分と二酸化炭素に対して、個々の輸送モデル、およびそれらを連成させた数理モデルの適切性を考察した。これらの結果は、数値的な解析を保証する上で重要な結果であると考える。また、本研究においては、巨視的領域と微視的領域を扱う二重尺度法を導入した数理モデルの適切性を構築した。こうした二重尺度法を用いた解析が足掛かりとなり、多孔質媒体のように、巨視的変化と微視的変化を伴う非線形現象の解析が進展していくと期待される。
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Report
(6 results)
Research Products
(31 results)
