Quasi-periodic solutions of forced Kirchhoff equation (Q523553)
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| Language | Label | Description | Also known as |
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| English | Quasi-periodic solutions of forced Kirchhoff equation |
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Quasi-periodic solutions of forced Kirchhoff equation (English)
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21 April 2017
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The author establishes the existence and the stability of small-amplitude quasi-periodic solutions with Sobolev regularity of the forced Kirchhoff equation \[ v_{tt}-\left(1+\int_{\mathbb{T}}(\partial_x v)^2dx\right)\partial_{xx} v=\delta f(\omega t,x), \] where \(x\in\mathbb{T}=\mathbb{R}/\mathbb{Z}\). The proof is based on a Nash-Moser scheme in Sobolev spaces.
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forced Kirchhoff equation
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quasi-periodic solution
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infinite-dimensional dynamical system
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KAM theory
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Nash-Moser theory
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