Long time behaviour for generalized complex Ginzburg–Landau equation |
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Authors: | Donglong Li Zhengde Dai Xuhong Liu |
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Affiliation: | aGuangxi Institute of Technology, Liuzhou 545006, PR China;bYunnan University, Kunming 650091, PR China |
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Abstract: | In this paper, the two-dimensional generalized complex Ginzburg–Landau equation (CGL)ut= ρu−Δ φ( u)−(1+ iγ)Δ u− νΔ 2u−(1+ iμ)| u| 2σu+ αλ1![dot operator dot operator](http://www.sciencedirect.com/scidirimg/entities/22c5.gif) ![backward difference backward difference](http://www.sciencedirect.com/scidirimg/entities/2207.gif) (| u| 2u)+ β( λ2![dot operator dot operator](http://www.sciencedirect.com/scidirimg/entities/22c5.gif) ![backward difference backward difference](http://www.sciencedirect.com/scidirimg/entities/2207.gif) )| u| 2 | is studied. The existence of global attractor for this equation with periodic boundary condition is established and upper bounds of Hausdorff and fractal dimensions of attractor are obtained.
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Keywords: | Generalized complex Ginzburg– Landau equation Global attractor Fractal dimension |
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