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Error estimates for the Ginzburg-Landau approximation

  • Guido Schneider
Original Papers

Abstract

Modulation equations play an essential role in the understanding of complicated dynamical systems near the threshold of instability. Here we look at systems defined over domains with one unbounded direction and show that the Ginzburg-Landau equation dominates the dynamics of the full problem, locally, at least over a long time-scale. As an application of our approximation theorem we look here at Bénard's problem. The method we use involves a careful handling of critical modes in the Fourier-transformed problem and an estimate of Gronwall's type.

Keywords

Dynamical System Error Estimate Essential Role Mathematical Method Critical Mode 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Copyright information

© Birkhäuser Verlag 1994

Authors and Affiliations

  • Guido Schneider
    • 1
  1. 1.Institut für Angewandte MathematikUniversität HannoverHannoverGermany

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