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Homogenization of trajectory attractors of Ginzburg-Landau equations with randomly oscillating terms

  • * Corresponding author: G. A. Chechkin

    * Corresponding author: G. A. Chechkin 

Work of GAC was supported in part by the Committee of Science of the Ministry of Education and Science of the Republic of Kazakhstan (grant no. AP05131707) and by the Russian Foundation for Basic Research (projects 18-01-00046). This research of VVC was supported by the Ministry of Education and Science of the Russian Federation (grant 14.Z50.31.0037). The work of LSP was partially supported by Russian Science Foundation (grant no. 18-11-00148).

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  • We consider complex Ginzburg-Landau (GL) type equations of the form:

    ${\partial _t}u = (1 + \alpha i)\Delta u + R{\mkern 1mu} u + (1 + \beta i)|u{|^2}u + g,$

    where $R$, $β$, and $g$ are random rapidly oscillating real functions. Assuming that the random functions are ergodic and statistically homogeneous in space variables, we prove that the trajectory attractors of these systems tend to the trajectory attractors of the homogenized equations whose terms are the average of the corresponding terms of the initial systems.

    Bibliography: 52 titles.

    Mathematics Subject Classification: Primary: 35B40, 35B41, 35B45, 35Q30.


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  • Figure 1.  Attractors of the Ginzburg-Landau Equations

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