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Second-Kind Equilibrium States of the Kuramoto–Sivashinsky Equation with Homogeneous Neumann Boundary Conditions

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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.

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Authors and Affiliations

  1. Yaroslavl State University, Yaroslavl, Russia

    A. V. Sekatskaya

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  1. A. V. Sekatskaya
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Correspondence to A. V. Sekatskaya.

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Translated from Itogi Nauki i Tekhniki, Seriya Sovremennaya Matematika i Ee Prilozheniya. Tematicheskie Obzory, Vol. 168, Proceedings of the International Conference “Geometric Methods in the Control Theory and Mathematical Physics” Dedicated to the 70th Anniversary of Prof. S. L. Atanasyan, 70th Anniversary of Prof. I. S. Krasil’shchik, 70th Anniversary of Prof. A. V. Samokhin, and 80th Anniversary of Prof. V. T. Fomenko. Ryazan State University named for S. Yesenin, Ryazan, September 25–28, 2018. Part I, 2019.

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Sekatskaya, A.V. Second-Kind Equilibrium States of the Kuramoto–Sivashinsky Equation with Homogeneous Neumann Boundary Conditions. J Math Sci 262, 844–854 (2022). https://doi.org/10.1007/s10958-022-05863-3

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  • DOI: https://doi.org/10.1007/s10958-022-05863-3

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