2011 Fiscal Year Final Research Report
Analysis of micro local structure of hyperbolic equations and characterization of hyperbolic equations for which the Cauchy problem is well-posed
| Project/Area Number |
20540155
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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 | University of Tsukuba |
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Principal Investigator |
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| Project Period (FY) |
2008 – 2011
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| Keywords | 双曲型作用素 / コーシー問題 / C^∞適切性 / 2階双曲型方程式 |
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| Research Abstract |
I considered the Cauchy problem for second-order hyperbolic operators with the coefficients of their principal parts depending only on the time variable. In the case where the coefficients 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 part are semi-algebraic functions (e. g., polynomials) of the time variable. Moreover, under this sufficient condition I proved that the singularities of solutions to the Cauchy problem propagate along broken null bicharacteristics.
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