| Project/Area Number |
12640166
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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 |
Basic analysis
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| Research Institution | Gifu University |
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Principal Investigator |
AIKI Toyohiko Gifu University, Faculty of Education, Associate Professor, 教育学部, 助教授 (90231745)
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| Co-Investigator(Kenkyū-buntansha) |
SATO Naoki Nagoya College of Technology, Associate Professor, 一般教育科, 助教授 (90280370)
TAKEUCHI Shigeru Gifu University, Professor, 教育学部, 教授 (30021330)
KENMOCHI Nobuyuki Chiba University, Professor, 教育学部, 教授 (00033887)
ITO Akio Kinki University, Lecturer, 工学部, 講師 (30303506)
YAMADA Masahiro Gifu University, Associate Professor, 教育学部, 助教授 (00263666)
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| Project Period (FY) |
2000 – 2001
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| Project Status |
Completed (Fiscal Year 2001)
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| Budget Amount *help |
¥3,700,000 (Direct Cost: ¥3,700,000)
Fiscal Year 2001: ¥1,800,000 (Direct Cost: ¥1,800,000)
Fiscal Year 2000: ¥1,900,000 (Direct Cost: ¥1,900,000)
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| Keywords | hysteresis operator / Shape memory alloys / nonlinear PDE's / 1相ステファン問題 / 最急降下法 / 最適制御問題 |
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| Research Abstract |
Several mathematicians and physicists already proposed some mathematical models consisting of partial differential equations in order to describe dynamics of shape memory alloy materials. In all of them they approximated the relationship between the strain and the stress by polynomials and functions and derived the models. However, in some experiments we know that the relationship is not a usual function and can be express by hysteresis operator, which depends on the historical data. Hence, in this research project we have proposed a new mathematical model including a hysteresis operator without polynomial approximation and studied the model by using the theory for evolution equations governed by time-dependent subdifferentials of convex functions on Hubert spaces. First, we considered the following problem. We already have known that the hysteresis operator is characterized by ordinary differential equations including the subdifferential operator of the indicator function. Then we added the ordinary differential equation to the system consisting of momentum balance law and internal energy balance law. A solution of this system may not satisfy the A smoothness condition so that we approximate the ordinary differential eauations by replacing the parabolic. Our first result is to prove the existence anu uniqueness theorem concerned witn sucn an approximated problem. Next, we applied the classical theory for parabolic equations to our system and showed the wellposedness of our problem without any approximations.
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