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Volume 17, Issue 1
Existence of Periodic Solutions for 3-D Complex Ginzberg-Landau Equation

Donglong Li & Boling Guo

J. Part. Diff. Eq., 17 (2004), pp. 12-28.

Published online: 2004-02

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  • Abstract
In this paper, the authors consider complex Ginzburg-Landau equation (CGL) in three spatial dimensions u_t = ρu + (1 + iϒ)Δu - (1 + iμ) |u|^{2σ u + f, where u is an unknown complex-value function defined in 3+1 dimensional space-time R^{3+1}, Δ is a Laplacian in R^3, Δ > 0, ϒ, μ are real parameters, Ω ∈ R^3 is a bounded domain. By using the method of Galërkin and Faedo-Schauder fix point theorem we prove the existence of approximate solution uN of the problem. By establishing the uniform boundedness of the norm ||uN|| and the standard compactness arguments, the convergence of the approximate solutions is considered. Moreover, the existence of the periodic solution is obtained .
  • Keywords

complex Ginzburg-Landau equation Galërkin method approximate solution time periodic solution

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@Article{JPDE-17-12, author = {Donglong Li and Boling Guo }, title = {Existence of Periodic Solutions for 3-D Complex Ginzberg-Landau Equation}, journal = {Journal of Partial Differential Equations}, year = {2004}, volume = {17}, number = {1}, pages = {12--28}, abstract = { In this paper, the authors consider complex Ginzburg-Landau equation (CGL) in three spatial dimensions u_t = ρu + (1 + iϒ)Δu - (1 + iμ) |u|^{2σ u + f, where u is an unknown complex-value function defined in 3+1 dimensional space-time R^{3+1}, Δ is a Laplacian in R^3, Δ > 0, ϒ, μ are real parameters, Ω ∈ R^3 is a bounded domain. By using the method of Galërkin and Faedo-Schauder fix point theorem we prove the existence of approximate solution uN of the problem. By establishing the uniform boundedness of the norm ||uN|| and the standard compactness arguments, the convergence of the approximate solutions is considered. Moreover, the existence of the periodic solution is obtained .}, issn = {2079-732X}, doi = {https://doi.org/}, url = {http://global-sci.org/intro/article_detail/jpde/5373.html} }
TY - JOUR T1 - Existence of Periodic Solutions for 3-D Complex Ginzberg-Landau Equation AU - Donglong Li & Boling Guo JO - Journal of Partial Differential Equations VL - 1 SP - 12 EP - 28 PY - 2004 DA - 2004/02 SN - 17 DO - http://doi.org/ UR - https://global-sci.org/intro/article_detail/jpde/5373.html KW - complex Ginzburg-Landau equation KW - Galërkin method KW - approximate solution KW - time periodic solution AB - In this paper, the authors consider complex Ginzburg-Landau equation (CGL) in three spatial dimensions u_t = ρu + (1 + iϒ)Δu - (1 + iμ) |u|^{2σ u + f, where u is an unknown complex-value function defined in 3+1 dimensional space-time R^{3+1}, Δ is a Laplacian in R^3, Δ > 0, ϒ, μ are real parameters, Ω ∈ R^3 is a bounded domain. By using the method of Galërkin and Faedo-Schauder fix point theorem we prove the existence of approximate solution uN of the problem. By establishing the uniform boundedness of the norm ||uN|| and the standard compactness arguments, the convergence of the approximate solutions is considered. Moreover, the existence of the periodic solution is obtained .
Donglong Li and Boling Guo . (2004). Existence of Periodic Solutions for 3-D Complex Ginzberg-Landau Equation. Journal of Partial Differential Equations. 17 (1). 12-28. doi:
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