Geodesic
Local Attractors in One Boundary-Value Problem for the Kuramoto--Sivashinsky Equation
Itogi nauki i tehniki. Sovremennaâ matematika i eë priloženiâ. Tematičeskie obzory, Proceedings of the International Conference “Geometric Methods in Control Theory and Mathematical Physics: Differential Equations, Integrability, and Qualitative Theory,” Ryazan, September 15–18, 2016, Tome 148 (2018), pp. 58-65

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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, normal forms, invariant manifolds, asymptotic formulas.
Mots-clés : bifurcations 
@article{INTO_2018_148_a7,
     author = {A. N. Kulikov and A. V. Sekatskaya},
     title = {Local {Attractors} in {One} {Boundary-Value} {Problem} for the {Kuramoto--Sivashinsky} {Equation}},
     journal = {Itogi nauki i tehniki. Sovremenna\^a matematika i e\"e prilo\v{z}eni\^a. Temati\v{c}eskie obzory},
     pages = {58--65},
     publisher = {mathdoc},
     volume = {148},
     year = {2018},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/INTO_2018_148_a7/}
}
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A. N. Kulikov; A. V. Sekatskaya. Local Attractors in One Boundary-Value Problem for the Kuramoto--Sivashinsky Equation. Itogi nauki i tehniki. Sovremennaâ matematika i eë priloženiâ. Tematičeskie obzory, Proceedings of the International Conference “Geometric Methods in Control Theory and Mathematical Physics: Differential Equations, Integrability, and Qualitative Theory,” Ryazan, September 15–18, 2016, Tome 148 (2018), pp. 58-65. http://geodesic.mathdoc.fr/item/INTO_2018_148_a7/