2017 Fiscal Year Final Research Report
Properties of solutions to dispersive equations
| Project/Area Number |
25400162
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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 | Osaka University |
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Principal Investigator |
DOI Shin-ichi 大阪大学, 理学研究科, 教授 (00243006)
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| Project Period (FY) |
2013-04-01 – 2018-03-31
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| Keywords | 分散型方程式 |
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| Outline of Final Research Achievements |
We studied the relations between various properties of solutions to linear dispersive equations and geometry of symbols of the equations. We considered the Cauchy problem for dispersive evolution equations with variable coefficients, which might be unbounded, of order greater than or equal to two on the Euclidean space, and obtained necessary conditions and sufficient conditions for the Cauchy problem to be well-posed. We also obtained new results on growth order of solutions to wave equations with time-dependent, spatially compact metric perturbations.
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| Free Research Field |
関数方程式
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