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

Voir la notice de l'article provenant de la source Math-Net.Ru

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 
@article{INTO_2023_226_a7,
     author = {A. N. Kulikov and D. A. Kulikov},
     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},
     pages = {69--79},
     publisher = {mathdoc},
     volume = {226},
     year = {2023},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/INTO_2023_226_a7/}
}
TY  - JOUR
AU  - A. N. Kulikov
AU  - D. A. Kulikov
TI  - Invariant manifolds and attractors of a periodic boundary-value problem for the Kuramoto--Sivashinsky equation with allowance for dispersion
JO  - Itogi nauki i tehniki. Sovremennaâ matematika i eë priloženiâ. Tematičeskie obzory
PY  - 2023
SP  - 69
EP  - 79
VL  - 226
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/INTO_2023_226_a7/
LA  - ru
ID  - INTO_2023_226_a7
ER  - 
%0 Journal Article
%A A. N. Kulikov
%A D. A. Kulikov
%T Invariant manifolds and attractors of a periodic boundary-value problem for the Kuramoto--Sivashinsky equation with allowance for dispersion
%J Itogi nauki i tehniki. Sovremennaâ matematika i eë priloženiâ. Tematičeskie obzory
%D 2023
%P 69-79
%V 226
%I mathdoc
%U http://geodesic.mathdoc.fr/item/INTO_2023_226_a7/
%G ru
%F INTO_2023_226_a7
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/