2001 Fiscal Year Final Research Report Summary
Study on phase transition problems with nonlinear control devices
| Project/Area Number |
11640223
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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 | Nagaoka National College of Technology |
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Principal Investigator |
SATO Naoki Nagaoka National College of Technology, Department of Math., AP, 一般教育科, 助教授 (90280370)
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| Co-Investigator(Kenkyū-buntansha) |
AIKI Toyohiko Gifu University, Faculty of Education, Department of Math., AP., 教育学部, 助教授 (90231745)
YAMADA Akira Nagaoka National College of Technology, Department of Math., AP, 一般教育科, 講師 (60311007)
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| Project Period (FY) |
1999 – 2000
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| Keywords | phase transition / dynamic boundary condition / optimal control / phase-field equation / descent methods / Stefan problem / 概エルミート多様体 / 等質多様体 |
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| Research Abstract |
We study a phase transition model of the phase field type in a vessel, which is a coupled system of two second order parabolic PDEs for temerature field and non-conserved order parameter. In order to control the order parameter, we use some control devices on the fixed boundary, which are usually described as a nonlinear boundary condition. In our study, we consider the dynamic boundary condition which includes the time derivative of temperature field on the fixed boundary. The purpose of our study is to prove existence and uniqueness of solutions with the well-posedness ina sufficiently large space. Our approach to this problem is based on the abstract theory of nonlinear evolution equations governd by time-dependent subdifferentials in Hilbert spaces.
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