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Exponential Attractor for Complex Ginzburg-Landau Equation in Three-dimensions
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@Article{JPDE-16-97,
author = {Boling Guo and Donglong Li },
title = {Exponential Attractor for Complex Ginzburg-Landau Equation in Three-dimensions},
journal = {Journal of Partial Differential Equations},
year = {2003},
volume = {16},
number = {2},
pages = {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.},
issn = {2079-732X},
doi = {https://doi.org/},
url = {http://global-sci.org/intro/article_detail/jpde/5409.html}
}
TY - JOUR
T1 - Exponential Attractor for Complex Ginzburg-Landau Equation in Three-dimensions
AU - Boling Guo & Donglong Li
JO - Journal of Partial Differential Equations
VL - 2
SP - 97
EP - 110
PY - 2003
DA - 2003/05
SN - 16
DO - http://doi.org/
UR - https://global-sci.org/intro/article_detail/jpde/5409.html
KW - Ginzburg-Landau equation
KW - exponential attractor
KW - squeezing property
AB - 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.
Boling Guo and Donglong Li . (2003). Exponential Attractor for Complex Ginzburg-Landau Equation in Three-dimensions.
Journal of Partial Differential Equations. 16 (2).
97-110.
doi:
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