| Project/Area Number |
23654052
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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 | Meiji University (2013-2014)
Osaka University (2011-2012) |
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Principal Investigator |
NAWA Hayato 明治大学, 理工学部, 教授 (90218066)
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| Co-Investigator(Kenkyū-buntansha) |
ISHIWATA Tetsuya 芝浦工業大学, システム工学部, 教授 (50334917)
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| Research Collaborator |
FIBICH Gadi Tel Aviv University, 教授
SULEM Catherine University Tronto, 教授
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| Project Period (FY) |
2011-04-28 – 2015-03-31
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| Project Status |
Completed (Fiscal Year 2014)
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| Budget Amount *help |
¥3,120,000 (Direct Cost: ¥2,400,000、Indirect Cost: ¥720,000)
Fiscal Year 2013: ¥910,000 (Direct Cost: ¥700,000、Indirect Cost: ¥210,000)
Fiscal Year 2012: ¥910,000 (Direct Cost: ¥700,000、Indirect Cost: ¥210,000)
Fiscal Year 2011: ¥1,300,000 (Direct Cost: ¥1,000,000、Indirect Cost: ¥300,000)
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| Keywords | 非線形シュレーディンガー方程式 / 爆発解 / ネルソン拡散過程 / 曲線の運動 / クリスタライン / 等位面 / 爆発速度 / ネルソン拡散課程 / 曲率流 / 等高面 / 国際研究者交流（イスラエル） / 解の爆発 / 非線形偏微分放映式 / 特異点 / 爆発解の延長 / シュレーディンガー方程式 |
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| Outline of Final Research Achievements |
This project was devoted to the study of the continuation problem of blowup solutions of the pseudo-conformally invariant nonlinear Schroedinger equation beyond the singularity. We tried to establish a rigorous mathematical concept to extend blowup solutions beyond the blowup time so that we investigated the precise behavior of the solution near the blowup time by means of the Nelson diffusion as well as a system of degenerate ordinary differential equations which had been found during the preparation of this project: the system of ODE describes the behavior of points in a level set of the square of the absolute value of the solution. Although we could not succeed to establish a significant concept of extending the blowup solutions, we obtained an estimate on the blowup rate for a class of blowup solutions and learned the importance of the numerical study to get an idea which lead us to a new KAKENHI project investing the blowup problem including other type of evolutional equations.
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