Coarsening by Ginzburg-Landau Dynamics
J. -p. Eckmann, Jacques Rougemont · 1998
. 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. Godr eche. Coarsening by Ginzburg-Landau 2 1. Introduction In a series of papers ([CP1,CP2]), Carr and Pego studied the evolution of multi-kink initial data of the real Ginzburg-Landau equation: @ t v = @ 2 x v + v \\Gamma v 3 = @ 2 x v + V 0 (v) ; (1:1) with v(x; t) : R \\Theta R + ! R: These data are for most x very close to the stationary values v = \\Sigma1 with transitions from \\Sigma1 to \\Upsilon1 at certain points. We call these points `kinks'. Since an isolated kink moves to the stable stationary solution tanh(x \\Gamma x 0 ) f...