2013 Fiscal Year Final Research Report
The refined diagonalization procedure and a development on the evolution equations with smooth coefficients
| Project/Area Number |
22540197
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| Research Category |
Grant-in-Aid for Scientific Research (C)
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| Allocation Type | Single-year Grants |
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| Section | 一般 |
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| Research Field |
Basic analysis
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| Research Institution | Yamaguchi University |
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Principal Investigator |
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| Project Period (FY) |
2010-04-01 – 2014-03-31
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| Keywords | 双曲型方程式 / 変数係数 / 波動方程式 / 非線形波動方程式 |
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| Research Abstract |
In this project, we studied evolution equations with smooth variable coefficients by using a special technique for the precise representations of the solutions, which is called "the refined diagonalization procedure". This method is very useful for the analysis of the initial values problems of hyperbolic equations with variable coefficients, for example, wave equations, Klein-Gordon type equations, second order hyperbolic equations and semi-linear wave equations. Indeed, we succeeded to prove some estimates for these problems, which couldn't be solved by using the previous method, by using our new method. Moreover, we expect that our results will be applicable for the analysis of non-linear problems, in particular, for the global solvability of Kirchhoff equation in non-realanalytic class.
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