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 |
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| Section | 一般 |
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| Research Field |
Mathematical analysis
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| Research Institution | Shimane University (2014-2016)
Kumamoto University (2013) |
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Principal Investigator |
Wada Takeshi 島根大学, 総合理工学研究科, 教授 (70294139)
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| Co-Investigator(Kenkyū-buntansha) |
中村 誠 山形大学, 理学部, 教授 (70312634)
北 直泰 熊本大学, 大学院先端科学研究部(工), 教授 (70336056)
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| Project Period (FY) |
2013-04-01 – 2017-03-31
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| Project Status |
Completed (Fiscal Year 2016)
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| Budget Amount *help |
¥4,290,000 (Direct Cost: ¥3,300,000、Indirect Cost: ¥990,000)
Fiscal Year 2016: ¥1,170,000 (Direct Cost: ¥900,000、Indirect Cost: ¥270,000)
Fiscal Year 2015: ¥1,170,000 (Direct Cost: ¥900,000、Indirect Cost: ¥270,000)
Fiscal Year 2014: ¥650,000 (Direct Cost: ¥500,000、Indirect Cost: ¥150,000)
Fiscal Year 2013: ¥1,300,000 (Direct Cost: ¥1,000,000、Indirect Cost: ¥300,000)
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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 / 非線形偏微分方程式 / 非線形 Schrodinger 方程式 / Strichartz 評価 / 偏微分方程式の適切性 / 非線形シュレディンガー方程式 / 解の時空間評価 |
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| 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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Report
(5 results)
Research Products
(42 results)
