Study of structure of solutions to Schrodinger equation from quantum-fluid point of view
Project/Area Number |
24740108
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Research Category |
Grant-in-Aid for Young Scientists (B)
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Allocation Type | Multi-year Fund |
Research Field |
Global analysis
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Research Institution | Hiroshima University |
Principal Investigator |
Masaki Satoshi 広島大学, 工学(系)研究科(研究院), 准教授 (20580492)
|
Project Period (FY) |
2012-04-01 – 2016-03-31
|
Project Status |
Completed (Fiscal Year 2015)
|
Budget Amount *help |
¥4,160,000 (Direct Cost: ¥3,200,000、Indirect Cost: ¥960,000)
Fiscal Year 2015: ¥1,040,000 (Direct Cost: ¥800,000、Indirect Cost: ¥240,000)
Fiscal Year 2014: ¥1,040,000 (Direct Cost: ¥800,000、Indirect Cost: ¥240,000)
Fiscal Year 2013: ¥1,040,000 (Direct Cost: ¥800,000、Indirect Cost: ¥240,000)
Fiscal Year 2012: ¥1,040,000 (Direct Cost: ¥800,000、Indirect Cost: ¥240,000)
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Keywords | 非線形シュレディンガー方程式 / 分散型方程式 / KdV 方程式 / 一般化KdV方程式 / 解の長時間挙動 / 最小化問題 / 最小爆発解 / 非線形偏微分方程式 / 一般化 KdV 方程式 / 散乱問題 / 最小非散乱解 / 非線型分散型方程式 / 非線型シュレディンガー方程式 / KdV方程式 / フーリエ制限問題 / シュレディンガー方程式 / 時間大域挙動 / 偏微分方程式 / 尺度不変空間 / 有限時間爆発 / 解の時間大域挙動 |
Outline of Final Research Achievements |
The first intend of the research was to focus on quantum-fluid properties of Schrodinger equations and to clarify the correspondence between blowup of solution to a nonlinear Schrodinger equation and collapse of solution of a corresponding classical fluid equation. The intended method for this analysis is a contradiction argument that construct a virtual solution from failure of a target conclusion. In this decade, there is much progress on this kind of argument. The research progresses unexpectedly and a special non-scattering solution which is minimal in a suitable sense is found for mass-subcritical equations. Behavior of the solution is completely unknown and different from any of those we knew before. I also consider generalized KdV equations and find that similar kind of threshold solution exists.
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Report
(5 results)
Research Products
(12 results)