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

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A boundary-value problem for the generalized Kuramoto–Sivashinsky equation with homogeneous Neumann boundary conditions is considered. The stability of spatially homogeneous equilibrium states are analyzed and local bifurcations at change of… Click to show full abstract

A boundary-value problem for the generalized Kuramoto–Sivashinsky equation with homogeneous Neumann boundary conditions is considered. The stability of spatially homogeneous equilibrium states are analyzed and local bifurcations at change of stability are studied. We use the method of invariant manifolds in combination with the theory of normal forms. Asymptotic formulas for bifurcating solutions are found.

Keywords: value problem; kuramoto sivashinsky; boundary value; sivashinsky equation

Journal Title: Journal of Mathematical Sciences
Year Published: 2020

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