2000 Fiscal Year Final Research Report Summary
Functional analytic study on global structures of nonlinear fields
| Project/Area Number |
09304012
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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 |
解析学
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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) |
HAYASHI Nakao Science Univ. of Tokyo, Fac. of Sci., Prof., 理学部, 教授 (30173016)
TSUTAYA Kinitoshi Hokkaido Univ., Grad. School of Sci., Asso. Prof., 大学院・理学研究科, 助教授 (60250411)
AGEMI Rentaro Hokkaido Univ., Grad. School of Sci., Prof., 大学院・理学研究科, 教授 (10000845)
NAKAMURA Makoto Tohoku Univ., Grad. School of Info. Sci., Research Associate, 大学院・情報科学研究科, 助手 (70312634)
TSUTSUMI Yoshio Tohoku Univ., Grad. School of Sci., Prof., 大学院・理学研究科, 教授 (10180027)
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| Project Period (FY) |
1997 – 2000
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| Keywords | Nonlinear wave equations / Nonlinear Klein-Gordon equations / Nonlinear Schrodinger equations / Nonlinear scattering theory / Regularity of solutions |
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| Research Abstract |
Mathematical reality and mechanism is studied on the nonlinear classical fields such as those described by nonlinear wave equations, nonlinear Klein-Gordon equations, and nonlinear Schrodinger equations. Special attention is given to global theories which are beyond the scope of available general theories. Small data scattering is proved for the above equations in the Sobolev spaces of any nonnegative order by specifying the associated critical nonlinearities. Large time behavior and regularity of solutions is also studied.
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