The Ginzburg᎐Landau-type complex partial differential equations are simplified mathematical models for various pattern formation systems in mechanics, physics, and chemistry. Most work so far concentrates on Ginzburg᎐Landau-type equations Ž . with one spatial dimension 1D . In this paper, the author
Asymptotics for the Generalized Two-Dimensional Ginzburg–Landau Equation
✍ Scribed by Hongjun Gao; Guoguang Lin; Jinqiao Duan
- Publisher
- Elsevier Science
- Year
- 2000
- Tongue
- English
- Weight
- 198 KB
- Volume
- 247
- Category
- Article
- ISSN
- 0022-247X
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✦ Synopsis
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 investigation of this type of model.
📜 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.
## Communicated by W. Eckhaus We consider parabolic systems defined on cylindrical domains close to the threshold of instability, in which the Fourier modes with positive growth rates are concentrated at a non-zero critical wave number. In particular, we consider systems for which a so-called Ginz
In this paper, we study a 2D generalized Ginzburg-Landau equation with a periodic boundary condition. The existence and uniqueness of a time-periodic solution to this equation is proved.