Geodesic
Invariant manifolds and attractors of a periodic boundary-value problem for the Kuramoto--Sivashinsky equation with allowance for dispersion
Itogi nauki i tehniki. Sovremennaâ matematika i eë priloženiâ. Tematičeskie obzory, Differential Equations and Mathematical Physics, Tome 226 (2023), pp. 69-79.

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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, boundary-value problem, stability, asymptotic formula.
Mots-clés : dispersion, bifurcation 
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     title = {Invariant manifolds and attractors of a periodic boundary-value problem for the {Kuramoto--Sivashinsky} equation with allowance for dispersion},
     journal = {Itogi nauki i tehniki. Sovremenna\^a matematika i e\"e prilo\v{z}eni\^a. Temati\v{c}eskie obzory},
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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. Itogi nauki i tehniki. Sovremennaâ matematika i eë priloženiâ. Tematičeskie obzory, Differential Equations and Mathematical Physics, Tome 226 (2023), pp. 69-79. http://geodesic.mathdoc.fr/item/INTO_2023_226_a7/

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