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- W1966395145 abstract "The behaviour as t → +∞ of solutions {u(x, t) ,t 0} of the non- autonomous Ginzburg-Landau (G.-L.) equation is studied. The main attention is focused on the case when the dispersion coefficient β(t) in this equation satisfies the inequality |β(t)| > √ 3f ort ∈ L ,w hereL is an unbounded subset of R+ .I n this case the uniqueness theorem for the G.-L. equation is not proved. The trajectory attractor A for this equation is constructed. If the coefficients and the exciting force are almost periodic (a.p.) in time and the uniqueness condition fails, then the trajectory attractor A is proved to consist precisely of the solutions {u(x, t) ,t 0} of the G.-L. equation that admit a bounded extension as solutions of this equation onto the entire time axis R. The behaviour as t → +∞ of solutions of a perturbed G.-L. equation with coefficients and the exciting force that are sums of a.p. functions and functions approaching zero in the weak sense as t → +∞ is also studied. Bibliography: 16 titles." @default.
- W1966395145 created "2016-06-24" @default.
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- W1966395145 date "2005-06-30" @default.
- W1966395145 modified "2023-09-23" @default.
- W1966395145 title "Non-autonomous Ginzburg-Landau equation and its attractors" @default.
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- W1966395145 doi "https://doi.org/10.1070/sm2005v196n06abeh000901" @default.
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