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Fixed points of a destabilized Kuramoto–Sivashinsky equation

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  • Bartha, Ferenc A.
  • Tucker, Warwick

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.

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  • Bartha, Ferenc A. & Tucker, Warwick, 2015. "Fixed points of a destabilized Kuramoto–Sivashinsky equation," Applied Mathematics and Computation, Elsevier, vol. 266(C), pages 339-349.
    • Handle: RePEc:eee:apmaco:v:266:y:2015:i:c:p:339-349
    DOI: 10.1016/j.amc.2015.05.082
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