2016 Fiscal Year Final Research Report
Study of nonlinear dispersive equations in critical Sobolev spaces
| Project/Area Number |
25800077
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| Research Category |
Grant-in-Aid for Young Scientists (B)
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| Allocation Type | Multi-year Fund |
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| Research Field |
Mathematical analysis
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| Research Institution | Shizuoka University |
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Principal Investigator |
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| Project Period (FY) |
2013-04-01 – 2017-03-31
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| Keywords | 非線形シュレディンガー方程式 / 散乱問題 / 基底状態の安定性 |
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| Outline of Final Research Achievements |
I studied a combined power-type nonlinear Schrodinger equation including the energy critical exponent. The aim is to reveal the behavior of the solutions starting from a neighborhood of a ground state. As a result, I proved that for any ground state with a sufficiently small frequency, the radial solutions starting from its neighbourhood exhibit one of the following scenarios: scattering to a free solution, blowup, or trapping by the ground state. Moreover, our proof clarifies the relation between potential wells with different frequencies.
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| Free Research Field |
偏微分方程式
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