| Project/Area Number |
24654034
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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 |
Basic analysis
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| Research Institution | Osaka University |
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Principal Investigator |
HAYASHI Nakao 大阪大学, 理学(系)研究科(研究院), 教授 (30173016)
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| Co-Investigator(Renkei-kenkyūsha) |
SUNAGAWA Hideaki 大阪大学, 大学院理学研究科, 准教授 (80375394)
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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 |
¥1,950,000 (Direct Cost: ¥1,500,000、Indirect Cost: ¥450,000)
Fiscal Year 2014: ¥650,000 (Direct Cost: ¥500,000、Indirect Cost: ¥150,000)
Fiscal Year 2013: ¥650,000 (Direct Cost: ¥500,000、Indirect Cost: ¥150,000)
Fiscal Year 2012: ¥650,000 (Direct Cost: ¥500,000、Indirect Cost: ¥150,000)
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| Keywords | 分散型波動方程式系 / 漸近的振舞い / 臨界べき非線形項 / 修正波動作用素 / Schroedinger方程式系 / Klein-Gordon方程式系 / 臨界冪非線形項 / Schredinger / Klein-Gordon / スケール不変 / 波動作用素 / 散乱状態 / 非線形分散型方程式系 / シュレデンガー方程式系 / クラインーゴルドン方程式系 / 散乱問題 / 双線形形式 / 分散型波動方程式 / 共鳴現象 / 時間減衰評価 |
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| Outline of Final Research Achievements |
We considered systems of nonlinear dispersive equations including nonlinear Schoedinger systems and nonlinear Klein-Gordon systems with quadratic interactions in two space dimensions. We showed the existence of modified wave operators for nonlinear Schroedinger systems under the mass resonance condition and non existence of wave operator by using a sharp time decay estimate of solutions to linear problem from below. For nonlinear Klein-Gordon systems, the initial value problem was considered when the initial data are in the class which is close to the energy one and the existence of scattering states was established under some mass non resonance conditions.
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