Stability of Moving Fronts in the Ginzburg-Landau Equation

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.

31 pages

Cited by in corpus (5)

• Existence and Stability of Propagating Fronts for an Autocatalytic Reaction-Diffusion System
• Renormalizing Partial Differential Equations
• Limit cycles in the presence of convection, a travelling wave analysis
• Spectral stability of pattern-forming fronts in the complex Ginzburg-Landau equation with a quenching mechanism
• Diffusive stability of Turing patterns via normal forms