EXISTENCE OF PERIODIC SOLUTIONS FOR 3-D COMPLEX GINZBERG-LANDAU EQUATION

• 来源期刊: 偏微分方程(英文版)
• 学科: 数学
• 关键词: complex Ginzburg-Landau equation Galerkin method approximate solution time periodic solution.
• 年，卷（期）: 2004,（1）
• 页码范围: 12-28
• 页数: 17页
• 分类号: O175.29.
• 语种: 英文

摘要

In this paper, the authors consider complex Ginzburg-Landau equation (CGL) in three spatial dimensions ut=ρu+(1+iγ) Δμ-(1+iμ) |u|2σu+f,where u is an unknown complex-value function defined in 3+1 dimensional space-time R3+1, Δ is a Laplacian in R3, ρ ＞ 0, γ, μ are real parameters, Ω ∈ R3 is a bounded domain. By using the method of Galerkin 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 .