Asymptotic analysis and inverse scattering of wave propagation problems in magnetic fields
| Project/Area Number |
25400179
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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 | Tokyo Metropolitan University |
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Principal Investigator |
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| Project Period (FY) |
2013-04-01 – 2016-03-31
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| Project Status |
Completed (Fiscal Year 2015)
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| Budget Amount *help |
¥4,680,000 (Direct Cost: ¥3,600,000、Indirect Cost: ¥1,080,000)
Fiscal Year 2015: ¥1,430,000 (Direct Cost: ¥1,100,000、Indirect Cost: ¥330,000)
Fiscal Year 2014: ¥1,430,000 (Direct Cost: ¥1,100,000、Indirect Cost: ¥330,000)
Fiscal Year 2013: ¥1,820,000 (Direct Cost: ¥1,400,000、Indirect Cost: ¥420,000)
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| Keywords | 磁場中のシュレディンガー作用素 / レゾルベントの一様評価 / 平滑化効果 / 散乱理論 / 散乱ｎ逆問題 / シュレディンガ―作用素 / レソルベント評価 / グラフ上の散乱問題 / Strichartz 評価 / 散乱振幅 / レゾナンス / レゾルベント評価 / グラフ上の散乱 / 散乱行列 |
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| Outline of Final Research Achievements |
In this project we are concerned with various wave propagation phenomena of dispersive evolution equations including the Schro"dinger equationｓ. The central object is in the uniform resolvent estimates for the magnetic Schro"dinger operators in extrior domain. Two dimensional problems is successfully solved, and we can now expect to develop several scattering problems of all dimensions. Especially, smoothing and Strichartz estimates are to be established to magnetic Klei-Gordon equations in exterior domain.
As for the one dimensional operators, the inverse problem to determine the potential from the scattering matrix is studied on several kind of unbounded star graphs. Coming study is concentrated to the graph which consists of a roop attached by several infinite rays.
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Report
(4 results)
Research Products
(22 results)
