Asymptotic analysis of water waves over a periodically oscillating bottom

2014 Fiscal Year Final Research Report

• Project/Area Number: 24340030
• Research Category: Grant-in-Aid for Scientific Research (B)
• Allocation Type: Partial Multi-year Fund
• Section: 一般
• Research Field: Global analysis
• Research Institution: Keio University
• Principal Investigator: IGUCHI Tatsuo 慶應義塾大学, 理工学部, 教授 (20294879)
• 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)
• Co-Investigator(Renkei-kenkyūsha): KAGEI Yoshiyuki 九州大学, 大学院数理学研究院, 教授 (80243913)
• Project Period (FY): 2012-04-01 – 2015-03-31
• Keywords: 水の波 / 水面波 / 浅水波 / 浅水波近似 / 長波長近似

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.

Free Research Field

数物系科学