Gallay, Th.
Local Stability of Critical Fronts in Non-linear
Parabolic Equations
(174K, Postscript)

ABSTRACT.  For the Ginzburg-Landau equation and similar non-linear
parabolic equations on the real line, we show the local
stability of the slowest monotonic front solution by
computing explicitly the leading term in the asymptotic
behavior of a small perturbation as $t \to \infty$. 
The proof is based on the Renormalization Group method
for parabolic equations.