Gevrey class regularity for the solutions of the Phase-Lock equations of Superconductivity
Mei-Qin Zhan
Conference Publications 2001, 2001(Special): 406-415 doi: 10.3934/proc.2001.2001.406
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keywords: Timeanalyticity Phase-Lock Equations. Gevrey class regularity Ginzburg-Landau (TDGL) Equations
Global attractors for phase-lock equations in superconductivity
Mei-Qin Zhan
Discrete & Continuous Dynamical Systems - B 2002, 2(2): 243-256 doi: 10.3934/dcdsb.2002.2.243
In previous article [18], we introduced a system of equations to model the superconductivity phenomena. We investigated its connection to Ginzburg-Landau equations and proved the existence and uniqueness of both weak and strong solutions. In this article, we study the dynamic behavior of solutions to the system and prove existence of global attractors and estimate their Hausdorff dimensions.
keywords: global attractors phase-lock equations. Ginzburg-Landau (TDGL) equations Hausdorff dimension
Finite element analysis and approximations of phase-lock equations of superconductivity
Mei-Qin Zhan
Discrete & Continuous Dynamical Systems - B 2002, 2(1): 95-108 doi: 10.3934/dcdsb.2002.2.95
In [22], the author introduced the phase-lock equations and established existences of both strong and weak solutions of the equations. We also investigated the relations between phase-lock equations and Ginzburg-Landau equations of Superconductivity. In this paper, we present finite element analysis and computations of phase-lock equations. We derive the error estimates for both semi-discrete and fully discrete equations, including optimal $L^2$ and $H^1$ error estimates. In the fully discrete case, we use backward Euler method to discretize the time variable.
keywords: Time Dependent Ginzburg-Landau (TDGL) Equations error estimates finite element phase-pock equations optimal convergence backward Euler method. discrete equations

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