Reserch on the propagation of singularities of the solutions for nonlinear hyperbolic partial differential equations
| Project/Area Number |
15K17576
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| Research Category |
Grant-in-Aid for Young Scientists (B)
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| Allocation Type | Multi-year Fund |
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| Research Field |
Mathematical analysis
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| Research Institution | Kitasato University |
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Principal Investigator |
Ito Shingo 北里大学, 一般教育部, 教授 (40548145)
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| Research Collaborator |
Kato Keiichi
Kobayashi Masaharu
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| Project Period (FY) |
2015-04-01 – 2019-03-31
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| Project Status |
Completed (Fiscal Year 2018)
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| Budget Amount *help |
¥1,690,000 (Direct Cost: ¥1,300,000、Indirect Cost: ¥390,000)
Fiscal Year 2017: ¥520,000 (Direct Cost: ¥400,000、Indirect Cost: ¥120,000)
Fiscal Year 2016: ¥520,000 (Direct Cost: ¥400,000、Indirect Cost: ¥120,000)
Fiscal Year 2015: ¥650,000 (Direct Cost: ¥500,000、Indirect Cost: ¥150,000)
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| Keywords | 波面集合 / 特異性伝播 / 波束変換 / 特異性の伝播 / モジュレーション空間 |
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| Outline of Final Research Achievements |
We obtained the characterization of the wavefront set by using the wave packet transform. Combining the characterization with the new representation of the solution to first-order hyperbolic partial differential equations with variable coefficients using wave packet transform, we given another proof of the theorem on propagation of singularities. On the other hand, by the method used above, we derive the new representation of the solution of linear dispersive partial differential equation including Schroedinger equation and Airy equation, and we obtained the some estimates of the solution on modulation space.
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| Academic Significance and Societal Importance of the Research Achievements |
波面集合の特徴付けに関しては，今回得られた波束変換による波面集合およびソボレフ型波面集合の特徴付けの他にも，F.B.I変換を用いたGabor型波面集合およびSG-波面集合の特徴付け，波束変換によるフーリエ・ルベーグ型波面集合の特徴付け等が知られているが，それらを偏微分方程式へ応用した結果はあまり知られていない。今回得られた結果は波束変換による波面集合の特徴付けを特異性の伝播の問題へ応用したものであり，結果自体は既知の結果であるが、ここで用いた手法は未解決問題にも適用可能であると考えられ，今後の発展が期待される。
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Report
(5 results)
Research Products
(6 results)
