2003 Fiscal Year Final Research Report Summary
GEOMETRY AND ANALYSIS FOR WAVE FIELDS
| Project/Area Number |
13304011
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| Research Category |
Grant-in-Aid for Scientific Research (A)
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| Allocation Type | Single-year Grants |
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| Section | 一般 |
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| Research Field |
Global analysis
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| Research Institution | Hokkaido University |
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Principal Investigator |
OZAWA Tohru Hokkaido Univ., Grad.School of Sci., Prof., 大学院・理学研究科, 教授 (70204196)
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| Co-Investigator(Kenkyū-buntansha) |
NAKAMURA Gen Hokkaido Univ., Grad.School of Sci., Prof., 大学院・理学研究科, 教授 (50118535)
TSUTSUMI Yoshio Kyoto Univ., Grad.School of Sci., Prof., 大学院・理学研究科, 教授 (10180027)
HAYASHI Nakao Osaka Univ., Grad.School of Sci., Prof., 大学院理学研究科, 教授 (30173016)
NAKANISHI Kenji Nagoya Univ., Grad.School of Math., Asso.Prof., 大学院・多元数理科学研究科, 助教授 (40322200)
TAKAOKA Hideo Kobe Univ., Faculty of Science, Asso.Prof., 理学部, 助教授 (10322794)
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| Project Period (FY) |
2001 – 2003
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| Keywords | nonlinear wave equations / nonlinear Dirac equations / nonlinear Klein-Gordon equations / nonlinear Schrodinger equations / scattering theory |
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| Research Abstract |
In this research project, various space-time behavior of solutions to nonlinear dispersive equations, such as nonlinear Schrodinger equations (NLS) and KdV type equations, nonlinear hyperbolic equations, such as nonlinear wave and Klein-Gordon equations, and coupled systems of those equations, such as nonlinear field equations. The main results are the following :
(1)Asymptotic completeness in the energy space H^1(R^3) for NLS with repulsive case has been proved.
(2)A unified treatment for small data scattering for nonlinear field equations has been given in terms of critical and subcritical setting.
(3)Existence and uniqueness of self-similar solutions for nonlinear wave equations have been proved in the framework of weak Lebesgue spaces.
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Research Products
(10 results)
