Chaos in the Kuramoto-Sivashinsky equations -- a computer-assisted proof. (Q1414013)
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scientific article; zbMATH DE number 2005886
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | Chaos in the Kuramoto-Sivashinsky equations -- a computer-assisted proof. |
scientific article; zbMATH DE number 2005886 |
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Chaos in the Kuramoto-Sivashinsky equations -- a computer-assisted proof. (English)
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19 November 2003
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The existence of infinitely many periodic solutions and symbolic dynamics is proved for the Kuramoto-Sivashinsky equation \(y'''+y'=1-{1\over 2}y^2\). It solves positively a problem posed by \textit{W. C. Troy} [J. Differ. Equations 82, 269--313 (1989; Zbl 0693.34053)]. The computer-assisted proof is based on symmetry arguments and Zgliczyński's covering relations method (compare \textit{G. Arioli} and \textit{P. Zgliczyński} [J. Differ. Equations 171, 173--202 (2001; Zbl 1018.37006)]).
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Kuramoto-Sivashinsky equation
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periodic solution
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symbolic dynamics
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covering relations
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