Analysis of differential equations on graphs.
| Project/Area Number |
23540181
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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 |
Basic analysis
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| Research Institution | Tohoku University |
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Principal Investigator |
TRUSHIN Igor 東北大学, 国際教育院, 准教授 (80600337)
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| Co-Investigator(Kenkyū-buntansha) |
KUBO Hideo 北海道大学, 理学 (系)研究科(研究院), 教授 (50283346)
MOCHIZUKI Hiyoshi 首都大学東京, 理工学研究科, 名誉教授 (80026773)
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| Project Period (FY) |
2011 – 2013
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| Project Status |
Completed (Fiscal Year 2013)
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| Budget Amount *help |
¥5,070,000 (Direct Cost: ¥3,900,000、Indirect Cost: ¥1,170,000)
Fiscal Year 2013: ¥1,430,000 (Direct Cost: ¥1,100,000、Indirect Cost: ¥330,000)
Fiscal Year 2012: ¥1,430,000 (Direct Cost: ¥1,100,000、Indirect Cost: ¥330,000)
Fiscal Year 2011: ¥2,210,000 (Direct Cost: ¥1,700,000、Indirect Cost: ¥510,000)
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| Keywords | 関数方程式 / 散乱理論 |
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| Research Abstract |
In this project we consider Schrodinger operators on noncompact graphs which consist of some infinite rays and compact part attached. Spectral and scattering problems on graphs arise as simplified models in mathematics, physics, chemistry and engineering when one considers the propagation of waves of different natures in thin, tube-like domains. We study scattering direct and inverse problems which are important in applied physics. (1)We treat an inverse scattering problem on a graph with an infinite ray and a loop joined at one point. Reconstruction procedure is presented.(2)We consider Schrodinger operators on noncompact star-shaped graphs including some finite rays. We show that our spectral representation formula provides the time dependent formulation of the scattering theory. The scattering operator is constructed in the configuration space, and then is related to the scattering matrix in the momentum space. Corresponding inverse scattering problem is investigated.
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Report
(4 results)
Research Products
(29 results)
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[Presentation] Scattering on graphs
Author(s)
I.Trushin
Organizer
Inverse and Ill-Posed Problems of Mathematical Physics
Place of Presentation
Novosibirsk University, Novosibirsk, Russia
Related Report
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