paper

Stability of Periodic Kuramoto-Sivashinsky Waves

arXiv:1012.4775

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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