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Itogi Nauki i Tekhniki. Sovremennaya Matematika i ee Prilozheniya. Tematicheskie Obzory, 2018, Volume 148, Pages 58–65 (Mi into303)  
This article is cited in 1 scientific paper (total in 1 paper)

Local Attractors in One Boundary-Value Problem for the Kuramoto–Sivashinsky Equation

A. N. Kulikov, A. V. Sekatskaya

P.G. Demidov Yaroslavl State University
Full-text PDF (183 kB) Citations (1)
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Abstract: A boundary-value problem for the generalized Kuramoto–Sivashinsky equation with homogeneous Neumann boundary conditions is considered in the paper. The analysis of stability of spatially homogeneous equilibrium states is given and local bifurcations are studied at the changes of their stability. When solving the problem, we use the method of invariant manifolds in combination with the theory of normal forms. The asymptotic formulas are found for bifurcating solutions.
Keywords: boundary value problems, stability, bifurcations, normal forms, invariant manifolds, asymptotic formulas.
English version:
Journal of Mathematical Sciences (New York), 2020, Volume 248, Issue 4, Pages 430–437
DOI: https://doi.org/10.1007/s10958-020-04883-1
Bibliographic databases:
Document Type: Article
UDC: 517.929
MSC: 35B32, 35B41
Language: Russian
Citation: A. N. Kulikov, A. V. Sekatskaya, “Local Attractors in One Boundary-Value Problem for the Kuramoto–Sivashinsky Equation”, Proceedings of the International Conference “Geometric Methods in Control Theory and Mathematical Physics: Differential Equations, Integrability, and Qualitative Theory,” Ryazan, September 15–18, 2016, Itogi Nauki i Tekhniki. Sovrem. Mat. Pril. Temat. Obz., 148, VINITI, M., 2018, 58–65; J. Math. Sci. (N. Y.), 248:4 (2020), 430–437
Citation in format AMSBIB
\Bibitem{KulSek18}
\by A.~N.~Kulikov, A.~V.~Sekatskaya
\paper Local Attractors in One Boundary-Value Problem for the Kuramoto--Sivashinsky Equation
\inbook Proceedings of the International Conference ``Geometric Methods in Control Theory and Mathematical Physics: Differential Equations, Integrability, and Qualitative Theory,'' Ryazan, September 15--18, 2016
\serial Itogi Nauki i Tekhniki. Sovrem. Mat. Pril. Temat. Obz.
\yr 2018
\vol 148
\pages 58--65
\publ VINITI
\publaddr M.
\mathnet{http://mi.mathnet.ru/into303}
\mathscinet{http://mathscinet.ams.org/mathscinet-getitem?mr=3847708}
\transl
\jour J. Math. Sci. (N. Y.)
\yr 2020
\vol 248
\issue 4
\pages 430--437
\crossref{https://doi.org/10.1007/s10958-020-04883-1}
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    • This publication is cited in the following 1 articles:
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    		Itogi Nauki i Tekhniki. Sovremennaya Matematika i ee Prilozheniya. Tematicheskie Obzory Itogi Nauki i Tekhniki. Sovremennaya Matematika i ee Prilozheniya. Tematicheskie Obzory
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