| Project/Area Number |
15K13461
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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 | Shibaura Institute of Technology |
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Principal Investigator |
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| Co-Investigator(Kenkyū-buntansha) |
齊藤 宣一 東京大学, 大学院数理科学研究科, 教授 (00334706)
名和 範人 明治大学, 理工学部, 専任教授 (90218066)
佐々木 多希子 早稲田大学, グローバルエデュケーションセンター, 助手 (30780150)
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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 |
¥3,900,000 (Direct Cost: ¥3,000,000、Indirect Cost: ¥900,000)
Fiscal Year 2017: ¥1,170,000 (Direct Cost: ¥900,000、Indirect Cost: ¥270,000)
Fiscal Year 2016: ¥1,170,000 (Direct Cost: ¥900,000、Indirect Cost: ¥270,000)
Fiscal Year 2015: ¥1,560,000 (Direct Cost: ¥1,200,000、Indirect Cost: ¥360,000)
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| Keywords | 数値解析 / 解の爆発 / 爆発レート / 領域爆発 / 爆発曲線 / 再爆発現象 / 確率微分方程式 / 関数微分方程式 / スケール不変性 / 爆発解 / 非線型現象 / 微分方程式 / 爆発オーダー / 爆発領域 / 非線形偏微分方程式 / 数値計算法 |
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| Outline of Final Research Achievements |
Blow-up phenomena are typical nonlinear phenomena in several mathematical models. Here “blow-up” means that a size of the solution becomes infinity in a finite time, that is, the solution has a singularity. In this research project, we focus on blow-up curves, regional blow-up and multiple blow-up in some partial differential equations. In these phenomena it is important to understand the geometric properties of the solutions in time-space plane, the strength of the singularity(blow-up rate), and their relations. We show some numerical methods to these topics and get many numerical observations. Moreover, we show mathematical results on some of those numerical conjectures.
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