Abstract
We are interested in the nonlinear stability of the Eckhaus-stable equilibria of the Swift-Hohenberg equation on the infinite line with respect to small integrable perturbations. The difficulty in showing stability for these stationary solutions comes from the fact that their linearizations possess continuous spectrum up to zero. The nonlinear stability problem is treated with renormalization theory which allows us to show that the nonlinear terms are irrelevant, i.e. that the fully nonlinear problem behaves asymptotically as the linearized one which is under a diffusive regime.
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Communicated by A. Kupiainen
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Schneider, G. Diffusive stability of spatial periodic solutions of the Swift-Hohenberg equation. Commun.Math. Phys. 178, 679–702 (1996). https://doi.org/10.1007/BF02108820
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DOI: https://doi.org/10.1007/BF02108820