On the Ginzburg-Landau model in the presence of an externally imposed magnetic field

关于存在外加磁场的金兹堡-朗道模型

• 批准号: 09650082
• 负责人: TSUTSUMI Masayoshi
• 金额: $ 1.92万
• 依托单位: Waseda University
• 依托单位国家: 日本
• 项目类别: Grant-in-Aid for Scientific Research (C)
• 财政年份: 1997
• 资助国家: 日本
• 起止时间: 1997 至 2000
• 项目状态: 已结题
• 来源: https://kaken.nii.ac.jp/grant/KAKENHI-PROJECT-09650082/
• 关键词: Ginzburg-Landau equation; superconductor; Meissner effect; semigroup theory; Galerkin's methods; initial-boundary value problem; difference methods; critical magnetic field; 超電導; Ginzburg-Landau eq.; 数理モデル; 非係形現象; Ginzburg-Landau; 非線形現象; 超電導

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.

1. 在外加磁场作用下，超导体镶嵌态的一种现象学描述方法可以考虑在磁场完全从超导体部分驱逐的约束下，吉布斯自由能的最小化问题。研究了时变Ginzburg-Landau-Maxwell方程的初边值问题。利用Fadeo-Galerkin方法建立了L_2弱解或强解的整体存在唯一性定理。对于抛物型问题，用半群方法得到了有界问题和外部问题L_3解的局部存在性。利用有限差分方法，得到了随时间变化的抛物型Ginzburg-Landan-Maxwell方程的数值解。

项目成果

M.Tsutsumi,H.Kasai: "The Mei Meissner effect and the Ginzburg-Landau equations in the presence of ………"GAKUTO Internat.Ser.Math.Sci.Appl.. 11. 311-321 (1998)

M.Tsutsumi, H.Kasai：“Mei Meissner 效应和 Ginzburg-Landau 方程在……的存在下”GAKUTO Internat.Ser.Math.Sci.Appl.. 11. 311-321 (1998)

M.Tsutsumi, H.Kasai: "The time dependent Ginzburg-Landau Maxwell equations" Nonlinear Analysis,T.M.A.(to appear). (1998)

M.Tsutsumi、H.Kasai：“时间相关的 Ginzburg-Landau Maxwell 方程”非线性分析，T.M.A.（即将出现）。

I Shislmarer. M.Tsutsumi. E.Kaikine: "Asymptotics in time for nonlinear nolocal Schrolnger equations with a source."J.Math.Soc.Japan. 51. 463-483 (1999)

我是希斯尔玛尔。

M.Tsutsumi,H.Kasai: "The Meissner effect and the Ginzburg-Landau equations in the presence of an applied magnetic field" Gakuto Internat.Ser.Math.Sci.Appl. 11. 311-321 (1998)

M.Tsutsumi，H.Kasai：“存在外加磁场时的迈斯纳效应和 Ginzburg-Landau 方程”Gakuto Internat.Ser.Math.Sci.Appl。

H.Nawa, M.Tsutsumi: "On Blow-up for the Psendo-Conformally Imriant Nonlinear Schivodinyer Equation II" Communications on Pure and Applied Mathematics. (to appear). (1998)

H.Nawa，M.Tsutsumi：“关于 Psendo-Conformally Imriant 非线性 Schivodinyer 方程 II 的放大”纯粹与应用数学通讯。