In this paper, we establish the global fast dynamics for the time-dependent Ginzburg}Landau equations of superconductivity. We show the squeezing property and the existence of "nite-dimensional exponential attractors for the system. In addition we prove the existence of the global attractor in ¸;¸ f
Asymptotics for the Time Dependent Ginzburg–Landau Equations
✍ Scribed by Jishan Fan; Shijin Ding
- Publisher
- Elsevier Science
- Year
- 1999
- Tongue
- English
- Weight
- 126 KB
- Volume
- 152
- Category
- Article
- ISSN
- 0022-0396
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📜 SIMILAR VOLUMES
Let W be a bounded, simply connected, regular domain of R N , N \ 2. For 0 < e < 1, let u e : W Q C be a smooth solution of the Ginzburg-Landau equation in W with Dirichlet boundary condition g e , i.e., ## ˛-Du in W, u e =g e on "W.
In this paper, the authors have studied a generalized Ginzburg᎐Landau equation Ž . in two spatial dimensions 2D . They have shown that this equation, under periodic boundary conditions, has the maximal attractor with finite Hausdorff dimension. This rigorously establishes the foundation for further
## Abstract Continuous dependence on a modelling parameter are established for solutions to a problem for a complex Ginzburg–Landau equation. We establish continuous dependence on the coefficient of the cubic term, and also on the coefficient of the term multiplying the Laplacian. Copyright 2003 Jo