Skip to main content
SpringerLink
Log in

The time dependent amplitude equation for the Swift-Hohenberg problem

  • Published:
Communications in Mathematical Physics Aims and scope Submit manuscript

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(ɛ-2). For the proofs, we use techniques for nonlinear semigroups and oscillatory integrals.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Similar content being viewed by others

References

  1. Collet, P., Eckmann, J.-P.: Instabilities and fronts in extended systems. Princeton: Princeton University Press 1990

    Google Scholar 

  2. Collet, P., Eckmann, J.-P.: The existence of dendritic fronts. Commun. Math. Phys.107, 39–92 (1986)

    Google Scholar 

  3. Collet, P., Eckmann, J.-P.: The stability of modulated fronts. Helv. Phys. Acta60, 969–991 (1987)

    Google Scholar 

  4. Eckmann, J.-P., Wayne, C.E.: Propagating fronts and the center manifold theorem. Preprint

  5. Lang, S.: Introduction to differentiable manifolds. New York: Wiley 1962

    Google Scholar 

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

    Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Centre de Physique Théorique, Laboratoire UPR A14, CNRS, Ecole Polytechnique, F-91128, Palaiseau, France

    P. Collet

  2. Département de Physique Théorique, Université de Genève, CH-1211, Geneva 4, Switzerland

    J. -P. Eckmann

Authors
  1. P. Collet
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. J. -P. Eckmann
    View author publications

    You can also search for this author in PubMed Google Scholar

Additional information

Communicated by A. Jaffe

Dedicated to Res Jost and Arthur Wightman

Rights and permissions

Reprints and permissions

About this article

Cite this article

Collet, P., Eckmann, J.P. The time dependent amplitude equation for the Swift-Hohenberg problem. Commun.Math. Phys. 132, 139–153 (1990). https://doi.org/10.1007/BF02278004

Download citation

  • Received:

  • Revised:

  • Issue Date:

  • DOI: https://doi.org/10.1007/BF02278004

Keywords

Search

Navigation