A New Estimate for the Ginzburg-Landau Approximation on the Real Axis

@inproceedings{Schneider2006ANE,
  title={A New Estimate for the Ginzburg-Landau Approximation on the Real Axis},
  author={Guido Schneider},
  year={2006}
}
Modulation equations play an essential rote in the understanding of complicated systems near the threshold of instability. For scalar parabolic equations for which instability occurs at nonzero wavelength, we show that the associated GinzburgLandau equation dominates the dynamics of the nonlinear problem locally, at least over a long timescale. We develop a method which is simpler than previous ones and allows initial conditions of lower regularity. It involves a careful handling of the… CONTINUE READING

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References

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Showing 1-6 of 6 references

Finite bandwidth , finite amplitude convection

J. Whitehead Newetl
Proc . Roy . Soc . Edinburgh Sect . A • 1992

On the validity of Ginzburg-Landau's equation

A. van Harten
Universit~it • 1992

The validity of modulation equations for extended systems with cubic nonlinearities

G. Schneider R Kirrmann, A. Mielke
The Ginzburg - Landau equation is an attractor • 1992

extended systems with cubic nonlinearities

A. Newetl, J. Whitehead
Proc. Roy. Soc. Edinburgh Sect. A • 1992

Partielle Differentialgleichungen

J. Wloka
Teubner, Stuttgart, • 1982

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