| Project/Area Number |
09304019
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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 |
General mathematics (including Probability theory/Statistical mathematics)
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| Research Institution | University of Tokyo |
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Principal Investigator |
MATANO Hiroshi School of Mathematical Sciences University of Tokyo, Graduate Professor, 大学院・数理科学研究科, 教授 (40126165)
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| Co-Investigator(Kenkyū-buntansha) |
YAMAMOTO Masahiro ditto, Associate Professor, 大学院・数理科学研究科, 助教授 (50182647)
YANAGIDA Eiji ditto, Associate Professor, 大学院・数理科学研究科, 助教授 (80174548)
FUNAKI Tadahisa ditto, Professor, 大学院・数理科学研究科, 教授 (60112174)
TANIGUCHI Masaharu Faculty of Science, Tokyo Institute of Technology, Lecturer, 大学院・情報理工学研究科, 講師 (30260623)
MIMURA Masayasu Graduate School of Science Hiroshima University, Professor, 大学院・理学研究科, 教授 (50068128)
堤 誉志雄 東京大学, 大学院・数理科学研究科, 助教授 (10180027)
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| Project Period (FY) |
1997 – 1999
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| Project Status |
Completed (Fiscal Year 1999)
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| Budget Amount *help |
¥21,500,000 (Direct Cost: ¥21,500,000)
Fiscal Year 1999: ¥4,200,000 (Direct Cost: ¥4,200,000)
Fiscal Year 1998: ¥7,600,000 (Direct Cost: ¥7,600,000)
Fiscal Year 1997: ¥9,700,000 (Direct Cost: ¥9,700,000)
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| Keywords | nonlinear partial differential equations / qualitative theory / diffusion equations / infinite dimensional dynamical systems / parabolic equations / attractor / 特異性 / 非線形偏微分方程式 / 漸近的方法 / 解の爆発 / 特異極限 / 界面 / 拡散方程式 / 無限次元力学系 / 順序保存力学系 / 進行波 / 特異摂動問題 / 自由境界 / 大域アトラクター |
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| Research Abstract |
(1) Dynamics of blow-up solutions Some blow-up solutions of a nonlinear heat equation can be continued beyond the blow-up time in a certain weak sense. Matano studied the dynamics of such solutions from the point of view of dynamical systems.
(2) Motion of interfaces with random deviation In a class of diffusion equations involving a small parameter, say ε, solutions develop sharp transition layers, or interfaces, as ε→0. Funaki considered the case where the equation involves a random deviation term.
(3) Estimate of blow-up time in a nonlinear heat equation Yanagida sutdied blow-up phenomena in a nonlinear heat equation and extended the classical results of Fujita and others.
(4) Motion of interface in competition systems Mimura studied the behavior of interfaces that arise in the singular limit of a three-species competition-diffusion system.
(5) Order-preserving systems in the presence of symmetry Matano extended the existing theory on order-preserving dynamical systems in the presence of symmetry. He then applied the general theory to the stability analysis of traveling waves and other problems.
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