Stability of Vortices and Numerical Analysis of Ginzburg-Landau Equation

涡稳定性与Ginzburg-Landau方程的数值分析

• 批准号: 11640141
• 负责人: MORITA Yoshihisa
• 金额: $ 2.37万
• 依托单位: Ryukoku University
• 依托单位国家: 日本
• 项目类别: Grant-in-Aid for Scientific Research (C)
• 财政年份: 1999
• 资助国家: 日本
• 起止时间: 1999 至 2000
• 项目状态: 已结题
• 来源: https://kaken.nii.ac.jp/grant/KAKENHI-PROJECT-11640141/
• 关键词: Ginzburg-Landau eguation; vortex; stability; bifurcation structure; nonlinear partial differential equation; dynamical system; 渦糸解; 平衡解の安定性

We studied the stability and dynamics of vortices of the Ginzburg-Landau equation which arises as a model describing a macroscopic superconducting phenomenon. We first showed the existence and stability of a single vortex solution in a disk with a variable coefficient. Next, to investigate the motion law of vortices, we derive an explicit form of a singular limit equation as the parameter goes to infinity. By virtue of this form we obtained some dynamical properties of vortices.We also studied some dynamical system problems and solution structures of elliptic equation to obtain several new results.

我们研究了描述宏观超导现象的Ginzburg-Landau方程的稳定性和涡旋动力学。我们首先证明了变系数圆盘中单个涡旋解的存在性和稳定性。其次，为了研究涡旋的运动规律，我们导出了当参数趋于无穷大时奇异极限方程的显式形式。借助于这种形式，我们得到了涡旋的一些动力学性质。我们还研究了一些动力系统问题和椭圆型方程的解结构，得到了几个新的结果。

项目成果

Hilhorst,D.,Iida,M.,Mimura,M.Ninomiya,H.: "A competition-diffusion system approximation to the classical two-phase Stefan problem"Japan Journal of Industrial and Applied Mathematics. (掲載予定).

Hilhorst, D.、Iida, M.、Mimura, M. Ninomiya, H.：“经典两相 Stefan 问题的竞争扩散系统近似”，日本工业与应用数学杂志（待出版）。

Hilhorst, D., Iida, M., Mimura, M., Ninomiya, H.: "A competition-diffusion system approximation to the classical two-phase Stefan problem"Japan J.Indust.Appl.Math.. (to appear). (2001)

Hilhorst, D.、Iida, M.、Mimura, M.、Ninomiya, H.：“近似经典两相 Stefan 问题的竞争扩散系统”Japan J.Indust.Appl.Math..（待发表）

Jimbo,S.,Morita,Y.: "Notes on the limit equation of vortex motion for the Ginzburg-Landau equation with Neumann condition"Japan Journal of Applied Mathematics. Vol.18,No.2(掲載予定). (2001)

Jimbo, S.，Morita, Y.：“关于具有诺伊曼条件的 Ginzburg-Landau 方程的极限方程的注释”，日本应用数学杂志，第 18 卷，第 2 期（待出版）。 ）

Morishita,H.,Yanagida,E.,Yotsutani,S.: "Structure change of solutions for a scalar curvature equation"Differential Integral Equations. Vol.14,No.8(掲載予定). (2001)

Morishita, H.、Yanagida, E.、Yotsutani, S.：“标量曲率方程解的结构变化”微分积分方程第 14 卷，第 8 期（待出版）。

Morita,Y.,Dockery,J.,Pernarowski,M.: "Symmetry breaking homoclinic bifurcations in diffusively coupled equations"Journal of Dynamics and Differential Equations. (掲載予定).

Morita, Y.、Dockery, J.、Pernarowski, M.：“扩散耦合方程中的对称性破坏同宿分岔”《动力学与微分方程杂志》（待出版）。