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Communications in Mathematical Physics

, Volume 132, Issue 1, pp 139–153 | Cite as

The time dependent amplitude equation for the Swift-Hohenberg problem

  • P. Collet
  • J. -P. Eckmann
Article

Abstract

Precise estimates for the validity of the amplitude approximation for the swift-Hohenberg equation are given, in a fully time dependent framework. It is shown that small solutions of orderO(ɛ) which are modulated like stationary solutions have an evolution which is well described in the amplitude approximation for a time of orderO-2). For the proofs, we use techniques for nonlinear semigroups and oscillatory integrals.

Keywords

Neural Network Statistical Physic Complex System Nonlinear Dynamics Stationary Solution 
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References

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    Hörmander, L.: The analysis of linear partial differential operators. Berlin, Heidelberg, New York: Springer 1983–1985Google Scholar

Copyright information

© Springer-Verlag 1990

Authors and Affiliations

  • P. Collet
    • 1
  • J. -P. Eckmann
    • 2
  1. 1.Centre de Physique ThéoriqueLaboratoire UPR A14, CNRS, Ecole PolytechniquePalaiseauFrance
  2. 2.Département de Physique ThéoriqueUniversité de GenèveGeneva 4Switzerland

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