Stability of Moving Fronts in the Ginzburg-landau Equation

Bricmont, Jean;Kupiainen, Antti
(1994) Communications in Mathematical Physics — Vol. 159, n° 2, p. 287-318 (1994)

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Authors
  • Bricmont, JeanUCLouvain
    Author
  • Kupiainen, AnttiUCLouvain
    Author
Abstract
We use Renormalization Group ideas to study stability of moving fronts in the Ginzburg-Landau equation in one spatial dimension. In particular, we prove stability of the real fronts under complex perturbations. This extends the results of Aronson and Weinberger to situations where the maximum principle is inapplicable and constitutes a step in proving the general marginal stability hypothesis for the Ginzburg-Landau equation.
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Bricmont, J., & Kupiainen, A. (1994). Stability of Moving Fronts in the Ginzburg-landau Equation. Communications in Mathematical Physics, 159(2), 287-318. https://doi.org/10.1007/BF02102640 (Original work published 1994)