| Project/Area Number |
12640170
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| Research Category |
Grant-in-Aid for Scientific Research (C)
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| Allocation Type | Single-year Grants |
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| Section | 一般 |
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| Research Field |
Basic analysis
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| Research Institution | Kyoto University |
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Principal Investigator |
OKAJI Takashi Kyoto University, Associate professor, 大学院・理学研究科, 助教授 (20160426)
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| Co-Investigator(Kenkyū-buntansha) |
SHIGEKAWA Ichiro Kyoto University, Professor, 大学院・理学研究科, 教授 (00127234)
NISHIDA Takaaki Kyoto University, Professor, 大学院・理学研究科, 教授 (70026110)
IKAWA Mitsuru Kyoto University, Professor, 大学院・理学研究科, 教授 (80028191)
DOI Shin'ichi University of Tsukuba, Associate professor, 数学系, 助教授 (00243006)
TANIGUCHI Masahiko Kyoto University, Associate professor, 大学院・理学研究科, 助教授 (50108974)
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| Project Period (FY) |
2000 – 2001
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| Project Status |
Completed (Fiscal Year 2001)
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| Budget Amount *help |
¥3,700,000 (Direct Cost: ¥3,700,000)
Fiscal Year 2001: ¥1,800,000 (Direct Cost: ¥1,800,000)
Fiscal Year 2000: ¥1,900,000 (Direct Cost: ¥1,900,000)
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| Keywords | Schrodinger equation / Dirac equation / Maxwell equation / Absence of eigenvalues / Unique continuation / Propagation of singularities / Smoothing effects / Microlocal analysis / シュレディンガー方程式 |
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| Research Abstract |
The head investigator Okaji has investigated two fundamental properties, absence of eigenvalues for first order elliptic systems and propagation of singularities of solutions to Shrodinger equations. As for the first property, he has treated physically important systems, Dirac operator and stationary Maxwell operators. In a joint work with H. Kalf and 0. Yamada, he obtained a nice condition which assures the nonexistence of embedded eigenvalues in continuous spectrum for the Dirac operators with potential diverging at infinity. Furthermore, he has extended the result to Dirac type operators as well as Maxwell operators in a non-isotropic media. He has obtained also strong unique continuation property for Stokes equations. As for the second topic, he has invented a new approach to the study of propagation of singularities of solutions to Schrodinger equations. This approach is based on a microlocal conservation law that the Wigner transformation of the solution obeys. It is strongly connected to the wave packet transform of the solutions. As applications, he can clarify a fine structure of propagation of microlocal singularities of solutions to Schrodinger equations with vector potential as well as electric potential which may grow at the infinity. It includes smoothing effects, reconstruction of singularities and creation of singularities from oscillatory initial data.
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