Itogi Nauki i Tekhniki. Sovremennaya Matematika i ee Prilozheniya. Tematicheskie Obzory
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Itogi Nauki i Tekhniki. Sovremennaya Matematika i ee Prilozheniya. Tematicheskie Obzory, 2019, Volume 168, Pages 80–90
DOI: https://doi.org/10.36535/0233-6723-2019-168-80-90 (Mi into503) 		 
Second-kind equilibrium states of the Kuramoto–Sivashinsky equation with homogeneous Neumann boundary conditions

A. V. Sekatskaya

P.G. Demidov Yaroslavl State University
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DOI: https://doi.org/10.36535/0233-6723-2019-168-80-90
Abstract: 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.
Funding agency Grant number
Russian Foundation for Basic Research 18-01-00672
Ministry of Education and Science of the Russian Federation 1.5722.2017/8.9
This work was supported by the Russian Foundation for Basic Research (project No. 18-01-00672) and the Ministry of Education and Science of the Russian Federation (project No. 1.5722.2017/8.9).
Document Type: Article
UDC: 517.956.4
MSC: 37L10, 37L25, 37L65
Language: Russian
Citation: A. V. Sekatskaya, “Second-kind equilibrium states of the Kuramoto–Sivashinsky equation with homogeneous Neumann boundary conditions”, 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, Itogi Nauki i Tekhniki. Sovrem. Mat. Pril. Temat. Obz., 168, VINITI, Moscow, 2019, 80–90
Citation in format AMSBIB
\Bibitem{Sek19}
\by A.~V.~Sekatskaya
\paper Second-kind equilibrium states of the Kuramoto--Sivashinsky equation with homogeneous Neumann boundary conditions
\inbook 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
\serial Itogi Nauki i Tekhniki. Sovrem. Mat. Pril. Temat. Obz.
\yr 2019
\vol 168
\pages 80--90
\publ VINITI
\publaddr Moscow
\mathnet{http://mi.mathnet.ru/into503}
\crossref{https://doi.org/10.36535/0233-6723-2019-168-80-90}
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