Study of behavior of solutions to nonlinear dispersive equations
| Project/Area Number |
22740092
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| Research Category |
Grant-in-Aid for Young Scientists (B)
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| Allocation Type | Single-year Grants |
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| Research Field |
Basic analysis
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| Research Institution | Shizuoka University (2011-2012)
Ehime University (2010) |
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Principal Investigator |
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| Project Period (FY) |
2010 – 2012
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| Project Status |
Completed (Fiscal Year 2012)
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| Budget Amount *help |
¥3,900,000 (Direct Cost: ¥3,000,000、Indirect Cost: ¥900,000)
Fiscal Year 2012: ¥1,300,000 (Direct Cost: ¥1,000,000、Indirect Cost: ¥300,000)
Fiscal Year 2011: ¥1,170,000 (Direct Cost: ¥900,000、Indirect Cost: ¥270,000)
Fiscal Year 2010: ¥1,430,000 (Direct Cost: ¥1,100,000、Indirect Cost: ¥330,000)
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| Keywords | 関数方程式 / 非線形シュレディンガー方程式 / 散乱問題 / 基底状態 / 爆発問題 / 非線形分散型方程式 |
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| Research Abstract |
I have studied nonlinear dispersive equations. Especially, I studied nonlinear Schrodinger equations containing the energy-critical term, and proved the followings:
(1) Existence of unstable ground state in four dimensions and higher.
(2) Nonexistence of ground state in three dimension.
(3) Classification of the behavior of solutions below the ground state energy, in view of scattering and blowup
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Report
(4 results)
Research Products
(13 results)
