Fixed points of a destabilized Kuramoto–Sivashinsky equation

Ferenc A. Bartha and Warwick Tucker

Applied Mathematics and Computation, 2015, vol. 266, issue C, 339-349

Abstract: We consider the family of destabilized Kuramoto–Sivashinsky equations in one spatial dimension ut+νuxxxx+βuxx+γuux=αu for α, ν ≥ 0 and β,γ∈R. For certain parameter values, shock-like stationary solutions have been numerically observed. In this work we verify the existence of several such solutions using the framework of self-consistent bounds and validated numerics.

Keywords: Kuramoto–Sivashinsky equations; Boundary value problem; Galerkin projection; Self-consistent bounds; Rigorous computations; Interval arithmetic (search for similar items in EconPapers)
Date: 2015
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Persistent link: https://EconPapers.repec.org/RePEc:eee:apmaco:v:266:y:2015:i:c:p:339-349

DOI: 10.1016/j.amc.2015.05.082

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