Asymptotic analysis of water waves over a periodically oscillating bottom
| Project/Area Number |
24340030
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| Research Category |
Grant-in-Aid for Scientific Research (B)
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| Allocation Type | Partial Multi-year Fund |
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| Section | 一般 |
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| Research Field |
Global analysis
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| Research Institution | Keio University |
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Principal Investigator |
IGUCHI Tatsuo 慶應義塾大学, 理工学部, 教授 (20294879)
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| Co-Investigator(Kenkyū-buntansha) |
TANI Atusi 慶應義塾大学, 理工学部, 名誉教授 (90118969)
TAKAYAMA Masahiro 慶應義塾大学, 理工学部, 助教 (90338252)
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| Co-Investigator(Renkei-kenkyūsha) |
KAGEI Yoshiyuki 九州大学, 大学院数理学研究院, 教授 (80243913)
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| Project Period (FY) |
2012-04-01 – 2015-03-31
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| Project Status |
Completed (Fiscal Year 2014)
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| Budget Amount *help |
¥5,460,000 (Direct Cost: ¥4,200,000、Indirect Cost: ¥1,260,000)
Fiscal Year 2014: ¥1,690,000 (Direct Cost: ¥1,300,000、Indirect Cost: ¥390,000)
Fiscal Year 2013: ¥1,560,000 (Direct Cost: ¥1,200,000、Indirect Cost: ¥360,000)
Fiscal Year 2012: ¥2,210,000 (Direct Cost: ¥1,700,000、Indirect Cost: ¥510,000)
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| Keywords | 水の波 / 水面波 / 浅水波 / 浅水波近似 / 長波長近似 / 流体 / 関数方程式 / 変分構造 / Euler-Lagrange方程式 / 国際研究者交流 / フランス / 浅水波方程式 / Green-Naghdi方程式 / Boussinesq方程式 / 国際情報交換 / 中国 / 関数方程式論 |
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| Outline of Final Research Achievements |
We considered the shallow water and long wave approximations for water waves over a periodically oscillating bottom, whose horizontally spatial scale is ε. We analyzed the homogenized limit (ε→０) of the solution to the shallow water equations by the method of multiple scales and determined explicitly the behavior of the solution. We also analyzed the homogenized limit and the long wave limit at the same time to a Boussinesq type equation. Moreover, we clarified the structure of a model for water waves which is obtained by the use of the variational structure.
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Report
(4 results)
Research Products
(31 results)
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[Presentation] 水の波の方程式2014
Author(s)
井口 達雄
Organizer
非線形偏微分方程式 冬の学校 '14 in 札幌
Place of Presentation
北海道大学（北海道・札幌市）
Year and Date
2014-11-21 – 2014-11-22
Related Report
Invited
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