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On the Nature of Local Bifurcations of the Kuramoto–Sivashinsky Equation in Various Domains

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Abstract

We consider a nonlinear parabolic partial differential equation in the case where the unknown function depends on two spatial variables and time, which is a generalization of the well-known Kuramoto–Sivashinsky equation. We consider homogeneous Dirichlet boundary-value problems for this equation. We examine local bifurcations when spatially homogeneous equilibrium states change stability. We show that post-critical bifurcations are realized in the boundary-value problems considered. We obtain asymptotic formulas for solutions and examine the stability of spatially inhomogeneous solutions.

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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. 185, Proceedings of the All-Russian Scientific Conference “Differential Equations and Their Applications” Dedicated to the 85th Anniversary of Professor M. T. Terekhin. Ryazan State University named for S. A. Yesenin, Ryazan, May 17-18, 2019. Part 1, 2020.

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Sekatskaya, A.V. On the Nature of Local Bifurcations of the Kuramoto–Sivashinsky Equation in Various Domains. J Math Sci 281, 412–417 (2024). https://doi.org/10.1007/s10958-024-07115-y

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  • DOI: https://doi.org/10.1007/s10958-024-07115-y

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