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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| Project Status |
Completed (Fiscal Year 2017)
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| Budget Amount *help |
¥4,810,000 (Direct Cost: ¥3,700,000、Indirect Cost: ¥1,110,000)
Fiscal Year 2016: ¥1,040,000 (Direct Cost: ¥800,000、Indirect Cost: ¥240,000)
Fiscal Year 2015: ¥1,040,000 (Direct Cost: ¥800,000、Indirect Cost: ¥240,000)
Fiscal Year 2014: ¥1,040,000 (Direct Cost: ¥800,000、Indirect Cost: ¥240,000)
Fiscal Year 2013: ¥1,690,000 (Direct Cost: ¥1,300,000、Indirect Cost: ¥390,000)
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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 / 衝突積分項 / 平滑効果 / Wasserstein 距離 / Tosacani 型距離 / Debye・湯川ポテンシャル / 測度解 / 超局所解析 / 大域解 / Besov 空間 / 漸近安定性 / 解の正則性 / 時間局所解 |
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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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Report
(6 results)
Research Products
(42 results)
