EXPONENTIAL ATTRACTOR FOR COMPLEX GINZBURG-LANDAU EQUATION IN THREE-DIMENSIONS

• 来源期刊: 偏微分方程（英文版）
• 学科: 数学
• 关键词: Ginzburg-Landau equation exponential attractor squeezing property.
• 年，卷（期）: 2003,（2）
• 页码范围: 97-110
• 页数: 14页
• 分类号: O175.29.
• 语种: 英文

摘要

In this paper, we consider the complex Ginzburg-Landau equation (CGL) in three spatial dimensionsut = ρu + (1 + iγ)△u - (1 + iμ)|u|2σ u, (1)u(0, x)= u0(x), (2)where u is an unknown complex-value function defined in 3+1 dimensional space-time R3+1, △ is a Laplacian in R3, ρ＞ 0,γ,μ are real parameters. Ω∈ R3 is a bounded domain. We show that the semigroup S(t) associated with the problem (1), (2) satisfies Lipschitz continuity and the squeezing property for the initial-value problem (1), (2)with the initial-value condition belonging to H2(Ω), therefore we obtain the existence of exponential attractor.