| Project/Area Number |
17H02851
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| Research Category |
Grant-in-Aid for Scientific Research (B)
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| Allocation Type | Single-year Grants |
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| Section | 一般 |
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| Research Field |
Mathematical analysis
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| Research Institution | Kyushu University (2019-2020, 2022)
Tohoku University (2017-2018) |
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Principal Investigator |
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| Co-Investigator(Kenkyū-buntansha) |
眞崎 聡 大阪大学, 基礎工学研究科, 准教授 (20580492)
前田 昌也 千葉大学, 大学院理学研究院, 准教授 (40615001)
高田 了 九州大学, 数理学研究院, 准教授 (50713236)
生駒 典久 慶應義塾大学, 理工学部(矢上), 准教授 (50728342)
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| Project Period (FY) |
2017-04-01 – 2021-03-31
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| Project Status |
Completed (Fiscal Year 2022)
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| Budget Amount *help |
¥15,340,000 (Direct Cost: ¥11,800,000、Indirect Cost: ¥3,540,000)
Fiscal Year 2020: ¥3,510,000 (Direct Cost: ¥2,700,000、Indirect Cost: ¥810,000)
Fiscal Year 2019: ¥3,640,000 (Direct Cost: ¥2,800,000、Indirect Cost: ¥840,000)
Fiscal Year 2018: ¥4,030,000 (Direct Cost: ¥3,100,000、Indirect Cost: ¥930,000)
Fiscal Year 2017: ¥4,160,000 (Direct Cost: ¥3,200,000、Indirect Cost: ¥960,000)
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| Keywords | 関数方程式論 / 調和解析学 / 変分法 / 流体 / 漸近解析 |
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| Outline of Final Research Achievements |
Nonlinear dispersive partial differential equation is one of important class in the partial differential equations. Due to a complex interaction between dispersive and nonlinear effects in the equation, there is a wide variety of asymptotic behavior of solution, and it is difficult to study long time behavior of solution. In this research, we tried to gain a new insight on long time behavior of solution to nonlinear dispersive equation by analyzing concrete models via harmonic analysis and variational methods.
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| Academic Significance and Societal Importance of the Research Achievements |
非線形分散型方程式は, プラズマ物理や渦糸の運動などを記述する非線形シュレディンガー方程式や, 水面波の動きを記述するKorteweg-de Vries (KdV) 方程式に代表されるように, 物理学, 工学のさまざまなモデルとして現れる. したがって, 非線形分散型方程式の解の長時間挙動に関して本研究課題で得られた成果は, 数学のみならず, 物理学, 工学的にも意義があるものと思われる.
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