Geodesic
Second-kind equilibrium states of the Kuramoto--Sivashinsky equation with homogeneous Neumann boundary conditions
Itogi nauki i tehniki. Sovremennaâ matematika i eë priloženiâ. Tematičeskie obzory, Proceedings of the International Conference "Geometric Methods in Control Theory and Mathematical Physics" dedicated to the 70th anniversary of S.L. Atanasyan, the 70th anniversary of I.S. Krasilshchik, the 70th anniversary of A.V. Samokhin, and the 80th anniversary of V.T. Fomenko. S.A. Esenin Ryazan State University, Ryazan, September 25–28, 2018. Part 1, Tome 168 (2019), pp. 80-90

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In this paper, we consider the boundary-value problem for the Kuramoto–Sivashinsky equation with homogeneous Neumann conditions. The problem on the existence and stability of second-kind equilibrium states was studied in two ways: by the Galerkin method and by methods of the modern theory of infinite-dimensional dynamical systems. Some differences in results obtained are indicated.
Keywords: Kuramoto–Sivashinsky equation, boundary-value problem, equilibrium, stability, Galerkin method, computer analysis. 
@article{INTO_2019_168_a9,
     author = {A. V. Sekatskaya},
     title = {Second-kind equilibrium states of the {Kuramoto--Sivashinsky} equation with homogeneous {Neumann} boundary conditions},
     journal = {Itogi nauki i tehniki. Sovremenna\^a matematika i e\"e prilo\v{z}eni\^a. Temati\v{c}eskie obzory},
     pages = {80--90},
     publisher = {mathdoc},
     volume = {168},
     year = {2019},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/INTO_2019_168_a9/}
}
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A. V. Sekatskaya. Second-kind equilibrium states of the Kuramoto--Sivashinsky equation with homogeneous Neumann boundary conditions. Itogi nauki i tehniki. Sovremennaâ matematika i eë priloženiâ. Tematičeskie obzory, Proceedings of the International Conference "Geometric Methods in Control Theory and Mathematical Physics" dedicated to the 70th anniversary of S.L. Atanasyan, the 70th anniversary of I.S. Krasilshchik, the 70th anniversary of A.V. Samokhin, and the 80th anniversary of V.T. Fomenko. S.A. Esenin Ryazan State University, Ryazan, September 25–28, 2018. Part 1, Tome 168 (2019), pp. 80-90. http://geodesic.mathdoc.fr/item/INTO_2019_168_a9/