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Itogi Nauki i Tekhniki. Sovremennaya Matematika i ee Prilozheniya. Tematicheskie Obzory, 2023, Volume 226, Pages 69–79
DOI: https://doi.org/10.36535/0233-6723-2023-226-69-79 (Mi into1203) 		 
Invariant manifolds and attractors of a periodic boundary-value problem for the Kuramoto–Sivashinsky equation with allowance for dispersion

A. N. Kulikov, D. A. Kulikov

P.G. Demidov Yaroslavl State University
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DOI: https://doi.org/10.36535/0233-6723-2023-226-69-79
Abstract: A periodic boundary-value problem for the dispersive Kuramoto–Sivashinsky equation is considered. The stability of homogeneous equilibria is examined and an analysis of local bifurcations with a change in stability is performed. This analysis is based on the methods of the theory of dynamical systems with an infinite-dimensional space of initial conditions. Sufficient conditions for the presence or absence of invariant manifolds are found. Asymptotic formulas for some solutions are obtained.
Keywords: Kuramoto–Sivashinsky equation, dispersion, boundary-value problem, stability, bifurcation, asymptotic formula.
Funding agency Grant number
Ministry of Science and Higher Education of the Russian Federation 075-02-2022-886
This work was supported by the Ministry of Science and Higher Education of the Russian Federation (project No. 075-02-2022-886).
Document Type: Article
UDC: 517.929
MSC: 37L10, 37L15, 37L25
Language: Russian
Citation: A. N. Kulikov, D. A. Kulikov, “Invariant manifolds and attractors of a periodic boundary-value problem for the Kuramoto–Sivashinsky equation with allowance for dispersion”, Differential Equations and Mathematical Physics, Itogi Nauki i Tekhniki. Sovrem. Mat. Pril. Temat. Obz., 226, VINITI, Moscow, 2023, 69–79
Citation in format AMSBIB
\Bibitem{KulKul23}
\by A.~N.~Kulikov, D.~A.~Kulikov
\paper Invariant manifolds and attractors of a periodic boundary-value problem for the Kuramoto--Sivashinsky equation with allowance for dispersion
\inbook Differential Equations and Mathematical Physics
\serial Itogi Nauki i Tekhniki. Sovrem. Mat. Pril. Temat. Obz.
\yr 2023
\vol 226
\pages 69--79
\publ VINITI
\publaddr Moscow
\mathnet{http://mi.mathnet.ru/into1203}
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