| Project/Area Number |
17K05324
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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 | Osaka University |
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Principal Investigator |
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| Project Period (FY) |
2017-04-01 – 2022-03-31
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| Project Status |
Completed (Fiscal Year 2021)
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| Budget Amount *help |
¥4,030,000 (Direct Cost: ¥3,100,000、Indirect Cost: ¥930,000)
Fiscal Year 2019: ¥1,170,000 (Direct Cost: ¥900,000、Indirect Cost: ¥270,000)
Fiscal Year 2018: ¥1,300,000 (Direct Cost: ¥1,000,000、Indirect Cost: ¥300,000)
Fiscal Year 2017: ¥1,560,000 (Direct Cost: ¥1,200,000、Indirect Cost: ¥360,000)
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| Keywords | 局所化系 / 横断的狭義双曲系 / 強双曲系 / 超局所伝播錐 / 包合的 / シンプレクティック / 特異点集合 / 伝播錐 / Fourier積分作用素 / Gevrey クラス / 初期値問題 / 適切性 / 一様対角化 / Gevreyクラス / 横断的 / symplectic多様体 / 一様対角化可能 |
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| Outline of Final Research Achievements |
We have studied the Cauchy problem for first-order systems. Assuming that the set S of singular points of the characteristic variety is a smooth manifold and the characteristic values are real and semisimple, we have introduced transversally strictly hyperbolic systems as systems which are strictly hyperbolic in the directions transverse to S. If the microlocal propagation cone and S are compatible, we have proved that transversally strictly hyperbolic systems are strongly hyperbolic. On the other hand, if the microlocal propagation cone is incompatible with S, we have shown that transversally strictly hyperbolic systems are much more involved, using an interesting example.
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| Academic Significance and Societal Importance of the Research Achievements |
本研究では微分方程式系を研究し，系の r 次特性点で主シンボルが対角化可能のとき，局所化系が接束の接空間をr次特性多様体の接空間で割った商空間上の系として自然に定義され，局所化系が狭義双曲系で，r 次特性多様体が包合的あるいはシンプレクティック多様体のときには強双曲系になることを示した．局所化系を通じて，強双曲型方程式と強双曲系の違いを明らかにする結果であり，強双曲系の研究を進めるうえで一つの指標になると考えられる．
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