Coarsening by Ginzburg-Landau Dynamics

Abstract

We study slowly moving solutions of the real Ginzburg-Landau equation on the line, by a method due to J. Carr and R.L. Pego. These are functions taking alternately positive or negative values on large intervals. A consequence of our approach is that we can propose a rigorous derivation of a stochastic model of coarsening by successive elimination of the smallest interval, which was described in earlier work by A.J. Bray, B. Derrida and C. Godrèche.

30 pages, TeX + postscript figures

Cited by in corpus (4)

• Asymptotic properties of stochastic Cahn-Hilliard equation with singular nonlinearity and degenerate noise
• Stability of synchronization in dissipatively driven Frenkel-Kontorova models
• Large-time behavior of solutions of parabolic equations on the real line with convergent initial data
• Dynamics of kinks in the Ginzburg-Landau equation: Approach to a metastable shape and collapse of embedded pairs of kinks