2016 Fiscal Year Final Research Report
Well-poshness and asymptotic behaviour of solutions to nonlinear partial differential equations describing interaction between several fields
Project/Area Number |
25400176
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Research Category |
Grant-in-Aid for Scientific Research (C)
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Allocation Type | Multi-year Fund |
Section | 一般 |
Research Field |
Mathematical analysis
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Research Institution | Shimane University (2014-2016) Kumamoto University (2013) |
Principal Investigator |
Wada Takeshi 島根大学, 総合理工学研究科, 教授 (70294139)
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Project Period (FY) |
2013-04-01 – 2017-03-31
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Keywords | 非線形偏異聞方程式 / 分散型方程式 / 波動方程式 / 平滑化効果 / 適切性 / 解の漸近挙動 |
Outline of Final Research Achievements |
We studied the well-posedness and properties of solutions of nonlinear partial differential equations in mathematical physics. A given problem for a partial differential equation with initial or boundary conditions is called well-posed if the problem has a unique solution, and if the solution depends continuously on the data given in the problem. This is an important step to ensure that the equation correctly describes the phenomenon. In this research we mainly studied the nonlinear Schrodinger equation and proved the well-posedness thereof under almost best possible conditions. We also studied related problems such as differentiability of solutions to dispersive and wave equations, and smoothing property of magnetic Schrodinger equations.
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Free Research Field |
非線形偏微分方程式論
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