93-205 Gallay, Th.
Local Stability of Critical Fronts in Non-linear Parabolic Equations (174K, Postscript) Jul 22, 93
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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.

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