2017 Fiscal Year Final Research Report
The Boltzmann equation without angular cutoff and nonlinear microlocal analysis
| Project/Area Number |
25400160
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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 | Kyoto University |
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Principal Investigator |
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| Co-Investigator(Kenkyū-buntansha) |
清水 扇丈 京都大学, 人間・環境学研究科, 教授 (50273165)
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| Research Collaborator |
Lerner Nicolas パリ6大学, 数学科教授
Pravda-Starov Karel レンヌ大学, 数学科教授
Xu Chao-Jiang ルーアン大学, 数学科教授
Yang Tong 香港城市大学, 数学科教授
Cho Yong-Kum ソウル中央大学, 数学科教授
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| Project Period (FY) |
2013-04-01 – 2018-03-31
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| Keywords | ボルツマン方程式 / 衝突積分作用素 / 非切断近似 / 解の平滑化 / 確率測度解 / Toscani 型距離 / 時間大域解 / 非線形超局所解析 |
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| Outline of Final Research Achievements |
The Cauchy problem for the Boltzmann equation is discussed under the assumption in consideration of a long-range interaction of particles. When the particle distribution is homogeneous in space variables, the existence and the smoothing effect of measure-valued solutions are proved in almost all physically reasonable cases of collision cross sections. In the spatially inhomogeneous case, the time local solution and the time global solution are obtained in various function spaces. The micro-local analysis is an important tool in order to handle the Boltzmann collision integral operator with angular singularity.
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| Free Research Field |
偏微分方程式論
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