We consider a generalized nonlocal Ginzburg–Landau equation with periodic boundary conditions. For the corresponding initial-boundary value problem we prove the existence of a solution for all positive values of the evolution variable. We study the existence and properties of invariant manifolds. We extract a class of invariant manifolds the union of which forms a global attractor. We describe the structure of the attractor and find the Euclidean dimension of its components. In the metric of the space of initial conditions, we also study the Lyapunov stability and orbital stability of solutions that belong in the global attractor.
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Translated from Problemy Matematicheskogo Analiza 123, 2023, pp. 67-84.
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Kulikov, A.N., Kulikov, D.A. Invariant Manifolds. Global Attractor of a Generalized Version of the Nonlocal Ginzburg–Landau Equation. J Math Sci 270, 693–713 (2023). https://doi.org/10.1007/s10958-023-06381-6
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DOI: https://doi.org/10.1007/s10958-023-06381-6