Year: 2004
Journal of Partial Differential Equations, Vol. 17 (2004), Iss. 1 : pp. 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 .
You do not have full access to this article.
Already a Subscriber? Sign in as an individual or via your institution
Journal Article Details
Publisher Name: Global Science Press
Language: English
DOI: https://doi.org/2004-JPDE-5373
Journal of Partial Differential Equations, Vol. 17 (2004), Iss. 1 : pp. 12–28
Published online: 2004-01
AMS Subject Headings:
Copyright: COPYRIGHT: © Global Science Press
Pages: 17
Keywords: complex Ginzburg-Landau equation