| Project/Area Number |
09440069
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| Research Category |
Grant-in-Aid for Scientific Research (B)
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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 | Science University of Tokyo |
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Principal Investigator |
KOMATSU Hikosaburo Science Univ.of Tokyo, Fac.of Sci. Prof., 理学部第一部, 教授 (40011473)
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| Co-Investigator(Kenkyū-buntansha) |
KATO Keiichi Science Univ.of Tokyo, Fac.of Sci. Lect., 理学部第一部, 講師 (50224499)
HAYASHI Nakao Science Univ.of Tokyo, Fac.of Sci. Prof., 理学部第一部, 教授 (30173016)
OKAZAWA Noboru Science Univ.of Tokyo, Fac.of Sci. Prof., 理学部第一部, 教授 (80120179)
MIYACHI Akihiko Tokyo Women's Christ.U., Col.of Arts & Sci. Prof., 文理学部, 教授 (60107696)
NAKAMURA Gen Gumma Univ., Fac.of Eng. Prof., 工学部, 教授 (50118535)
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| Project Period (FY) |
1997 – 1999
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| Keywords | Hyperfunctions / Logarithms of operators / Nonlinear partial differential equations / Existence of solutions / Analyticity of solutions / Asymptotic behavior of solutions / Inverse problems for elasticity / Function spaces defined by real analysis |
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| Research Abstract |
The biggest achievement we have made for the last three years with the help of the Grant-in-Aid would be that we have created a very active group of researchers centered at the Kagurazaka Campus of the Science University of Tokyo. Since April, 1999, we are conducting an open seminar "Kagurazaka Seminar on Analysis" every month, in which three lectures are presented. We also had an international conference in November, 1999. The purpose of this research project was described as "to prepare Functional Analysis and Real Analysis so that necessary tools would be furnished for the research of partial differential equations and, in particular, to nonlinear equations". A big amount of results have been obtained along this line by not only the registered investigators of the project but also graduate students who worked with them and many of the attendants of the seminar and the international conference.
Besides revision and correction of an English translation of his books, Komatsu discovered a few new results on convolutions of hyperfunctions etc.
Okazawa applied abstract theories of linear evolution equations and nonlinear semigroups to concrete equations such as the Ginzburg-Landau equations. He also established a general theory of the logarithms log A of linear operators.
Hayashi and Kato studied nonlinear partial differential equations mainly of evolution type. Hayashi proved the existence of solutions and analyzed their asymptotic behavior as the time tends to infinity for many important equations. Kato established the analyticity of solutions.
Nakamura considered the inverse problem of elastic bodies and applied it to the tomography.
Miyachi has obtained basic results on function spaces which are defined by real analytic methods and are getting more and more important in the theory of differential equations.
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