2015 Fiscal Year Final Research Report
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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| 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 |
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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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| Free Research Field |
偏微分方程式
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