Attractors of derivative complex Ginzburg-Landau equation in unbounded domains |
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Authors: | Boling Guo Yongqian Han |
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Affiliation: | (1) Institute of Applied Physics and Computational Mathematics, Nonlinear Center for Studies, P. O. Box 8009, Beijing, 100088, China |
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Abstract: | The Ginzburg-Landau-type complex equations are simplified mathematical models for various pattern formation systems in mechanics, physics, and chemistry. In this paper, the derivative complex Ginzburg-Landau (DCGL) equation in an unbounded domain Ω ⊂ ℝ2 is studied. We extend the Gagliardo-Nirenberg inequality to the weighted Sobolev spaces introduced by S. V. Zelik. Applied this Gagliardo-Nirenberg inequality of the weighted Sobolev spaces and based on the technique for the semi-linear system of parabolic equations which has been developed by M. A. Efendiev and S. V. Zelik, the global attractor in the corresponding phase space is constructed, the upper bound of its Kolmogorov’s ɛ-entropy is obtained, and the spatial chaos of the attractor for DCGL equation in ℝ2 is detailed studied. |
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Keywords: | Derivative complex Ginzburg-Landau (DCGL) equation global attractor Kolmogorov’ s ɛ -entropy spatial chao |
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