Geodesic
Attractor of the generalized Cahn--Hilliard equation, on which all solutions are unstable
Itogi nauki i tehniki. Sovremennaâ matematika i eë priloženiâ. Tematičeskie obzory, Proceedings of the International Conference on Mathematical Modelling in Applied Sciences — ICMMAS'19. Belgorod, August 20–24, 2019, Tome 195 (2021), pp. 57-67

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We consider the generalized Сahn–Hilliard equation supplemented by periodic boundary conditions. For the considered boundary-value problem, we obtain sufficient conditions for the existence of a two-dimensional local attractor formed by time-periodic solutions that are unstable in the sense of A. M. Lyapunov. The study is based on asymptotic methods and some methods of the theory of infinite-dimensional dynamical systems, such as the method of integral manifolds and the theory of normal forms.
Mots-clés : Cahn–Hilliard equation, local bifurcation
Keywords: boundary-value problem, stability. 
@article{INTO_2021_195_a6,
     author = {A. N. Kulikov and D. A. Kulikov},
     title = {Attractor of the generalized {Cahn--Hilliard} equation, on which all solutions are unstable},
     journal = {Itogi nauki i tehniki. Sovremenna\^a matematika i e\"e prilo\v{z}eni\^a. Temati\v{c}eskie obzory},
     pages = {57--67},
     publisher = {mathdoc},
     volume = {195},
     year = {2021},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/INTO_2021_195_a6/}
}
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A. N. Kulikov; D. A. Kulikov. Attractor of the generalized Cahn--Hilliard equation, on which all solutions are unstable. Itogi nauki i tehniki. Sovremennaâ matematika i eë priloženiâ. Tematičeskie obzory, Proceedings of the International Conference on Mathematical Modelling in Applied Sciences — ICMMAS'19. Belgorod, August 20–24, 2019, Tome 195 (2021), pp. 57-67. http://geodesic.mathdoc.fr/item/INTO_2021_195_a6/