Year: 2003
Journal of Partial Differential Equations, Vol. 16 (2003), Iss. 2 : pp. 97–110
Abstract
In this paper, we consider the complex Ginzburg-Landau equation (CGL) in three spatial dimensions u_t = ρu + (1 + iϒ )Δu - (1 + iμ) |u|^{2σ} u, \qquad(1) u(0, x) = u_0(x), \qquad(2) where u is an unknown complex-value function defined in 3+1 dimensional space-time R^{3+1}, Δ is a Laplacian in R³, ρ > 0, ϒ, 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.
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Journal Article Details
Publisher Name: Global Science Press
Language: English
DOI: https://doi.org/2003-JPDE-5409
Journal of Partial Differential Equations, Vol. 16 (2003), Iss. 2 : pp. 97–110
Published online: 2003-01
AMS Subject Headings:
Copyright: COPYRIGHT: © Global Science Press
Pages: 14
Keywords: Ginzburg-Landau equation