2000 Fiscal Year Final Research Report Summary
On the Ginzburg-Landau model in the presence of an externally imposed magnetic field
| Project/Area Number |
09650082
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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 |
Engineering fundamentals
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| Research Institution | Waseda University |
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Principal Investigator |
TSUTSUMI Masayoshi Waseda University, School of Science and Engineering, Professor, 理工学部, 教授 (70063774)
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| Co-Investigator(Kenkyū-buntansha) |
ANADA Kouichi Waseda University, School of Science and Engineering, Researcher, 理工学部, 助手 (20287957)
IDOGAWA Tomoyuki Shibaura Institute of Technology, Faculty of Systems Engineering, Associate Professor, システム工学部, 講師 (40257225)
OTANI Mituharu Waseda University, School of Science and Engineering, Professor, 理工学部, 教授 (30119656)
ISHIWATA Tetuya Japan Society for the Promotion of Science , JFellow, 特別研究員
HIRATA Daisuke Waseda University, School of Science and Engineering, Researcher, 理工学部, 助手 (50318797)
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| Project Period (FY) |
1997 – 2000
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| Keywords | Ginzburg-Landau equation / superconductor / Meissner effect / semigroup theory / Galerkin's methods / initial-boundary value problem / difference methods / critical magnetic field |
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| Research Abstract |
1. It is shown that a way of phenomenological description of the mosaic state in a superconductor under an applied magnetic field leads to consider the minimizing problem of the Gibbs free energy under the constraints of complete expulsion of magnetic field from the parts of superconductor.
2. The initial-boundary value problem for the time-dependent Ginzburg-Landau-Maxwell equations is considered. The global existence and uniqueness theorems of L_2 weak or strong solutions are established via Fadeo-Galerkin's method. As to the parabolic version, the local existence of L_3 solutions is obtained by the semigroup approach for both bounded and exterior problems.
3. Numerical experiments of solutions to the parabolic version of the time dependent Ginzburg-Landan-Maxwell equations are obtained by the finite difference methods.
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