2000 Fiscal Year Final Research Report Summary
Modelling and analysis of nonlinear phenomena with phase transitions
| Project/Area Number |
11640197
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| Research Category |
Grant-in-Aid for Scientific Research (C)
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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 | Chiba University |
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Principal Investigator |
KENMOCHI Nobuyu Chiba University Fac.Education, Prof., 教育学部, 教授 (00033887)
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| Co-Investigator(Kenkyū-buntansha) |
KOSHIKAWA Hiroaki Chiba University Fac.Education, Prof., 教育学部, 教授 (60000866)
UZAWA Masakatsu Chiba University Fac.Education, Prof., 教育学部, 教授 (80009026)
KURANO Masami Chiba University Fac.Education, Prof., 教育学部, 教授 (70029487)
AIKI Toyohiko Gifu University Fac.Education, Ass.Prof, 教育学部, 助教授 (90231745)
OTANI Mitsuharu Waseda University Sch.Sci.Tech. Prof., 理工学部, 教授 (30119656)
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| Project Period (FY) |
1999 – 2000
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| Keywords | phase transition / subdifferentials / phase separation / Stefan problems / free boundary problems / attractors / 非線形発展方程式 / 安定性 |
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| Research Abstract |
In this project, various linear or nonlinear systems such as phase transition models And reaction-diffusion equations from the view-point of the linear or non-linear Operator theory, and a lot of results, which are of high level especially from an interdisciplinary point of view, has been established. For instance,
(1) A stability theory for a class of nonlinear systems of parabolic PDEs, which includes a mathematical model for solid-liquid phase transition in the mesoscopic length scale, was evolved. In this theory, a new concept "the local in space stability" was introduced. This is quite reasonable from the physical point of view ; in fact, within this concept the growth or disapprearance of phases are able to be theoretically explained.
(2) It is a very convenient mathematical approach to describe various nonlinear time dependent processes as (autonomous or nonautonomous) dynamical systems, when one wants to know the asymptotic behavior of the processes as time goes to infinity. There is a concept of global attractors of dynamical systems for this purpose. We established a general method for the construction of global attractors of dynamical processes of a class wide enough.
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