| Project/Area Number |
01460004
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| Research Category |
Grant-in-Aid for General Scientific Research (B)
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| Allocation Type | Single-year Grants |
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| Research Field |
解析学
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| Research Institution | University of Tokyo |
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Principal Investigator |
MASUDA Kyuya University of Tokyo, Faculty of Science, Pfofessor, 理学部, 教授 (10090523)
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| Co-Investigator(Kenkyū-buntansha) |
SHOJI Mayumi University of Tokyo, Faculty of Science, Assistant, 理学部, 助手 (10216161)
ISHIMURA Naoyuki University of Tokyo, Faculty of Science, Assistant, 理学部, 助手 (80212934)
FUKAYA Kenji University of Tokyo, Faculty of Science, Associate Professor, 理学部, 助教授 (30165261)
KATAOKA Kiyomi University of Tokyo, Faculty of Science, Associate Professor, 理学部, 助教授 (60107688)
MATANO Hiroshi University of ToKYO, Faculty of Science, Associate Professor, 理学部, 助教授 (40126165)
小林 俊行 東京大学, 理学部, 助手 (80201490)
小松 彦三郎 東京大学, 理学部, 教授 (40011473)
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| Project Period (FY) |
1989 – 1990
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| Project Status |
Completed (Fiscal Year 1990)
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| Budget Amount *help |
¥6,200,000 (Direct Cost: ¥6,200,000)
Fiscal Year 1990: ¥2,700,000 (Direct Cost: ¥2,700,000)
Fiscal Year 1989: ¥3,500,000 (Direct Cost: ¥3,500,000)
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| Keywords | reaction-diffusion system / nonlinear heat equation / blow-up of solutions / bifurcation theory / Riemannian manifold / water wave / 表面張力方程式 / 多様体上のベキレイ構造 / 非線型反応拡散系 / 非線型拡散方程式 / 楕円型方程式 / ラプラス変換 / 境界値混合問題 / 順序保存力学系 |
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| Research Abstract |
We have studied nonlinear partial differential equations from many aspects in the period 1989 May-1991 March. Masuda succeeded first in showing the existence of stable periodic solutions of reaction-diffusion systems of some type, the most important class of nonlinear parabolic equations. He also considered the heat equation in the form u=*u+a (x) u^p and showed any non-negative solution blows up in a finite time if a (x) is posive at some point in the domain considered. Matano considered the nonlinear heat equation in some one-dimensional space interval with Dirichlet boundary condition.
He could show the remarkable result that any solutions with a continuous function as the initial data blows up at a (at most) finite number of points.Ishimura showed the existence and nonexistence of multi-valued solutions of nonlinear elliptic equations of the form *u=u^p. shouji made research into the permanent progressive waves and analyzed the bifurcation of progressive waves. Fukaya made research into nonlinear differential equations in differential geometry. He clarified the structure of small ball in the Riemannian manifold with sectional curvature less than one in absolute value.
Kataoka succeeded in showing the hypoellipticity of degenerate elliptic equations.
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