Existence of Quasipattern Solutions of the Swift-Hohenberg Equation

Boele Braaksma*, Gerard Iooss, Laurent Stolovitch

*Corresponding author for this work

    Research output: Contribution to journalArticleAcademicpeer-review

    6 Citations (Scopus)

    Abstract

    We consider the steady Swift-Hohenberg partial differential equation, a one-parameter family of PDEs on the plane that models, for example, Rayleigh-B,nard convection. For values of the parameter near its critical value, we look for small solutions, quasiperiodic in all directions of the plane, and which are invariant under rotations of angle . We solve an unusual small divisor problem and prove the existence of solutions for small parameter values, then address their stability with respect to quasi-periodic perturbations.

    Original languageEnglish
    Pages (from-to)255-285
    Number of pages31
    JournalArchive for Rational Mechanics and Analysis
    Volume209
    Issue number1
    DOIs
    Publication statusPublished - Jul-2013

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