Initial and boundary value problems for nonlinear dispersive wave equations
| Project/Area Number |
19684002
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| Research Category |
Grant-in-Aid for Young Scientists (A)
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| Allocation Type | Single-year Grants |
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| Research Field |
Basic analysis
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| Research Institution | Tohoku University |
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Principal Investigator |
NAKAMURA Makoto 東北大学, 大学院・理学研究科, 准教授 (70312634)
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| Project Period (FY) |
2007 – 2010
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| Project Status |
Completed (Fiscal Year 2010)
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| Budget Amount *help |
¥10,400,000 (Direct Cost: ¥8,000,000、Indirect Cost: ¥2,400,000)
Fiscal Year 2010: ¥2,600,000 (Direct Cost: ¥2,000,000、Indirect Cost: ¥600,000)
Fiscal Year 2009: ¥2,600,000 (Direct Cost: ¥2,000,000、Indirect Cost: ¥600,000)
Fiscal Year 2008: ¥2,600,000 (Direct Cost: ¥2,000,000、Indirect Cost: ¥600,000)
Fiscal Year 2007: ¥2,600,000 (Direct Cost: ¥2,000,000、Indirect Cost: ¥600,000)
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| Keywords | 関数方程式 / 偏微分方程式 / 非線形 / 初期値問題 / 外部問題 / 消散型波動方程式 / 長時間解 / 時間大域解 / 零条件 / 境界値問題 / 波動方程式 / 適切性 / 非線形シュレディンガー方程式 / ストリッカーツ評価 / 非線形波動方程式 |
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| Research Abstract |
The well-posedness of the Cauchy problem for higher order dispersive wave equations was considered based on the generalization of the Keel-Smith-Sogge type estimate which is one of the weighted energy estimates for wave equations. The well-posedness of the Cauchy problem for higher order parabolic equations with power type nonlinear terms were constructed by the use of energy estimates for parabolic equations. Almost global solutions for localized dissipative wave equations with critical nonlinear terms were shown in exterior domains in three dimensional Euclidean spaces. And the global solutions were shown when the nonlinear terms satisfy the null conditions.
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Report
(6 results)
Research Products
(21 results)
