2017 Fiscal Year Final Research Report
Evolution equations with variable coefficients and their applications to Kirchhoff equation
| Project/Area Number |
26400170
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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 | Yamaguchi University |
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Principal Investigator |
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| Project Period (FY) |
2014-04-01 – 2018-03-31
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| Keywords | キルヒホフ方程式 / 非線形波動方程式 / 変数係数 / 発展方程式 / クライン・ゴルドン方程式 |
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| Outline of Final Research Achievements |
We study the global solvability to the Cauchy problem of nonlinear wave equation of Kirchhoff type in a certain class of ultradifferentiable functions, which is not included real-analytic class. We also study linear evolution equations with time dependent coefficients in particular the linear wave equation with time dependent propagation speed and the Klein-Gordon equation with time dependent mass. The former equation is a linearized model of Kirchhoff equation, and the analysis of it will be expected to apply the problem of Kirchhoff equation; indeed, our main result for Kirchhoff equation is due to a precise estimate for the linear wave equation. For the latter equation, we derive some energy estimates with oscillating mass around 0, which are not really trivial from the previous results. Both estimates for linear evolution equations are derived by precise analysis in the time-frequency space which is developed in the research of this project.
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| Free Research Field |
数学
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