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Existence of Periodic Solutions for Ginzburg–Landau Equations of Superconductivity
Journal of Mathematical Analysis and Applications, 2000 In an earlier paper (B. Wang, 1999, J. Math. Anal. Appl.232, 394–412) the author proved the existence of periodic solutions to the Ginzburg–Landau equations of superconductivity in two dimensions.
Mei-Qin Zhan
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Dynamic Bifurcation of the Ginzburg--Landau Equation
SIAM Journal on Applied Dynamical Systems, 2004Summary: We study in this article the bifurcation and stability of the solutions of the Ginzburg-Landau equation, using a notion of bifurcation called attractor bifurcation. We obtain in particular a full classification of the bifurcated attractor and the global attractor as \(\lambda\) crosses the first critical value of the linear problem ...
Tian Ma, Jungho Park, Shouhong Wang
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On the Ginzburg-Landau Wave Equation
Bulletin of the London Mathematical Society, 1990Consider the initial value problem of the Ginzburg-Landau wave equation with a general power self-interaction term: \[ (*)\quad \phi_ t=(1+i\alpha)\Delta \phi +(1+i\beta)\phi -(1+i\gamma)| \phi |^{\mu -1}\phi,\quad x\in {\mathbb{R}}^ n,\quad t>0, \] \[ \phi (x,0)=\phi_ 0(x),\quad x\in {\mathbb{R}}^ n, \] where \(\phi\) is a complex scalar function ...
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A Bifurcation Analysis for the Ginzburg-Landau Equation
Archive for Rational Mechanics and Analysis, 1998The authors consider the following boundary-value problem for the Ginzburg-Landau equation \[ \begin{aligned}-\Delta u={1\over\varepsilon^2} u_\varepsilon(1-|u_\varepsilon|^2)\quad &\text{in }B,\\ u_\varepsilon(z)= z^d\quad &\text{on }\partial B,\end{aligned}\tag{1} \] where \(B\) is the unit ball of \(\mathbb{R}^2\), \(d\in\mathbb{N}^*\) and ...
Comte, Myriam, Mironescu, Petru
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Long time behavior of the Ginzburg-Landau superconductivity equations
Applied Mathematics Letters, 1995 The existence, uniqueness and asymptotic behavior of the solutions of a nonstationary Ginzburg-Landau superconductivity model are discussed without assumption on the L∞ norm of the initial data.
Tang, Q., Wang, S.
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The Ginzburg–Landau equation for interfacial instabilities
Physics of Fluids A: Fluid Dynamics, 1992A coherent method for pursuing a numerical multiple scales analysis of an interface problem is presented. Finding numerical boundary conditions for the homogeneous adjoint problem and evaluation of surface terms in the inhomogeneous solvability criteria is reduced to one singular value decomposition. The method is applied to derive the complex Ginzburg–
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On the Burgers-Ginzburg-Landau equations
Communications in Nonlinear Science and Numerical Simulation, 1998zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Guo, Boling, Huang, Haiyang
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The Validity of Generalized Ginzburg-Landau Equations
Mathematical Methods in the Applied Sciences, 1996The work is devoted to a rigorous derivation of the Ginzburg-Landau (GL) equations as an asymptotic limit of nonlinear ultraparabolic equations describing systems of hydrodynamic origin, in which a stationary homogeneous state becomes unstable, at a critical value of a control parameter, against spatial perturbations with a finite wavelength.
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Ginzburg–Landau equations for superconductivity
2023Abstract This chapter presents the Ginzburg-Landau equations, which are the core of the phenomenological theory of superconductivity of Ginzburg and Landau. First it follows the historical path to describe the formalism of F. and H. London and derive their equations.
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Small energy solutions to the Ginzburg–Landau equation
Comptes Rendus de l'Académie des Sciences - Series I - Mathematics, 2000zbMATH Open Web Interface contents unavailable due to conflicting licenses.
F. Bethuel +2 more
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