2004 Fiscal Year Final Research Report Summary
Research on the structure and stability of the dynamical system describing phase transition phenomena
| Project/Area Number |
13440052
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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 |
Global analysis
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| Research Institution | Chiba University |
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Principal Investigator |
KENMOCHI Nobuyuki Chiba University, Faculty of Education, Professor, 教育学部, 教授 (00033887)
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| Co-Investigator(Kenkyū-buntansha) |
KURANO Masami Chiba University, Faculty of Education, Professor, 教育学部, 教授 (70029487)
KOSHIKAWA Hiroaki Chiba University, Faculty of Education, Professor, 教育学部, 教授 (60000866)
OTANI Mitsuharu Waseda Univ., School of Science & Technology, Professor, 理工学術院, 教授 (30119656)
AIKI Toyohiko Gifu University, Faculty of Education, Associate Professor, 教育学部, 助教授 (90231745)
ITO Akio Kinki University, Faculty of Engineering, Associate Professor, 工学部, 助教授 (30303506)
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| Project Period (FY) |
2001 – 2004
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| Keywords | phase transition / stability of dynamical system / Stefan problem / global attractor / subdifferential / nonlinear evolution equation |
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| Research Abstract |
The subjects of this project are the following :
(1)Modelings of phase transition phenomena with their mathematical theory
(2)Formulations of the related optimal control problems and numerical simulations
(3)Return of the research results to the school education
Concerning (1), on the basis of the fundamental laws of the thermo-mechanics, we investigated the structure (phase change, component separation, damage evolution, ordering of atoms) of materials from the view-point of the theory of dymanical systems. Especially, during the last two years (2003-2004) of the project, we treated a class of models for irreversible phase change phenomena, taking account of the process of damage, and evolved its mathematical theory. In our research the subdifferential theory, which have been accumulated for these 15 years, worked very well and we had a big progress more than we expected. Concerning (2), proposing some formulations of optimal control problems in which control parameters are described by a class of hysteresis functions, we finished almost the theoretical part of the problems and tried partially their numerical tests. It was pointed out that there are still some questions which should be improved. Many papers treating subjects (1)and (2)were published and we organized two international conferences during this research project.
As far as (3)is concerned, many practices were reported in the meetings "Mathematical analysis of phase transitions and their related mathematics education" which we organized every year. We paid our attention to time-dependent phenomena noticed easily in our daily lives, verifying very carefully their value-added educational aspects as teaching materials of mathematics or sciences for the secondary school. We expect that this research enables to provide new teaching materials by which students can perceive usefulness of mathematics.
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