Global behavior for nonlinear wave

2015 Fiscal Year Final Research Report

• Project/Area Number: 24340024
• Research Category: Grant-in-Aid for Scientific Research (B)
• Allocation Type: Partial Multi-year Fund
• Section: 一般
• Research Field: Basic analysis
• Research Institution: Hokkaido University
• Principal Investigator: Kubo Hideo 北海道大学, 理学(系)研究科(研究院), 教授 (50283346)
• Co-Investigator(Kenkyū-buntansha): KATAYAMA Soichiro 和歌山大学, 教育学部, 教授 (70283942) ; TAKAMURA Hiroyuki 公立はこだて未来大学, システム情報科学部, 教授 (40241781) ; HOSHIGA Akira 静岡大学, 工学部, 准教授 (60261400) ; NAKAMURA Makoto 山形大学, 理学部, 教授 (70312634) ; DOI Kazuyuki 富山県立大学, 工学部, 講師 (80608331)
• Project Period (FY): 2012-04-01 – 2016-03-31
• Keywords: 非線型波動方程式 / 漸近的に平坦な計量 / 時間大域解 / 解の爆発

Outline of Final Research Achievements

Our research is concerned with equations which describe the way of propagation of waves. More precisely, we study the nonlinear effect produced by the interaction among waves, as well as the effect coming from the structure of the space-time in which the wave exists. For instance, when there exists an obstacle in the space, we are able to show that the way of propagation of waves are similar to that for the case where there exists no obstacle. In particular, it is a big progress to solve this kind of problem in two space dimensional case.
Moreover, we also study the way of propagation of waves in the space-time equipped with the metric which describes the expanding universe. By considering the property of function which represents the wave in detail, we rigorously proved the following intuitive image: the wavelength of the waves become long, so that the waves are stabilized in such an expanding universe model.

Free Research Field

Partial Differential Equations