2014 Fiscal Year Final Research Report
Research on initial and boundary value problems, and space-time estimates for nonlinear partial differential equations
| Project/Area Number |
23684004
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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 |
Global analysis
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| Research Institution | Yamagata University (2013-2014)
Tohoku University (2011-2012) |
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Principal Investigator |
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| Project Period (FY) |
2011-04-01 – 2015-03-31
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| Keywords | 偏微分方程式 / 非線形 / 初期値問題 / 境界値問題 |
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| Outline of Final Research Achievements |
The space-time estimates by Lindblad and Rodnianski were generalized, and the initial value problem was considered for the system of wave equations with nonlinear terms which satisfy the null conditions in three spatial dimensions. The initial value problem was considered for heat equations with derivative nonlinear terms in Besov spaces and Triebel-Lizorkin spaces. The energy solutions of the initial value problem were constructed for nonlinear Klein-Gordon equations in the de Sitter space-time, and nonlinear Schroedinger equations derived by its nonrelativistic limit. The best constant of the Moser-Trudinger inequality was shown in Lebesgue spaces with a weight which has a singularity, and it is applied to the initial value problem for nonlinear Klein-Gordon equations with nonlinear terms of exponential type.
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| Free Research Field |
関数方程式論
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