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arXiv · 1012.4775

Stability of Periodic Kuramoto-Sivashinsky Waves

Blake Barker·Mathew A. Johnson·Pascal Noble·L. Miguel Rodrigues·Kevin Zumbrun
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Abstract

In this note, we announce a general result resolving the long-standing question of nonlinear modulational stability, or stability with respect to localized perturbations, of periodic traveling-wave solutions of the generalized Kuramoto-Sivashinsky equation, establishing that spectral modulational stability, defined in the standard way, implies nonlinear modulational stability with sharp rates of decay. The approach extends readily to other second- and higher-order parabolic equations, for example, the Cahn-Hilliard equation or more general thin film models.

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Blake Barker, Mathew A. Johnson, Pascal Noble, L. Miguel Rodrigues, Kevin Zumbrun. 2010-12-21. Stability of Periodic Kuramoto-Sivashinsky Waves. https://arxiv.org/abs/1012.4775

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