2015 Fiscal Year Final Research Report
Characterization of hyperbolic operators for which the Cauchy problem is well-posed in the framework of infinitely differentiable functions
| Project/Area Number |
23540185
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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 |
Basic analysis
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| Research Institution | University of Tsukuba |
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Principal Investigator |
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| Project Period (FY) |
2011-04-28 – 2016-03-31
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| Keywords | 双曲型作用素 / コーシー問題 / Ｃ∞適切性 / 超局所解析 |
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| Outline of Final Research Achievements |
I considered the Cauchy problem for higher-order hyperbolic operators with coefficients depending only on the time variable. In the case where the coefficients of the principal parts are real analytic functions of the time variable, I obtained a sufficient condition for C∞ well-posedness. And I showed that this sufficient condition is also a necessary one when the space dimension is less than 3 or the coefficients of the principal parts are semi-algebraic functions ( e.g., polynomials ) of the time variable. Moreover, in the case where the coefficients of the lower-order terms also depend on the space variables, I obtained a similar results under restrictions on the number of the double characteristic roots.
I gave sufficient conditions for C∞ well-posedness of the Cauchy problem for third-order hyperbolic operators whose coefficients depend only on the time variable, in the form of imposing conditions on the subprincipal symbols and the first-order terms.
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| Free Research Field |
数学・基礎解析学
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