 9846 S. Brassesco, P. Butta'
 Interface fluctuations for the d=1 stochastic GinzburgLandau equation
with nonsymmetric reaction term
(306K, PostScript)
Feb 4, 98

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Abstract. We consider a GinzburgLandau equation in the
interval $[\eps^{1},\eps^{1}]$, $\eps>0$,
with Neumann boundary conditions,
perturbed by an additive white noise of strength
$\sqrt \eps$, and reaction term being the derivative of a
function which has two equal depth wells at $\pm1$,
but is not symmetric. When $\eps=0$, the equation has equilibrium
solutions that are increasing, and connect $1$ with $+1$. We call
them instantons, and we study the evolution of the solutions of the
perturbed equation in the limit $\eps\to 0^+$ , when the initial
datum is close to an instanton. We prove that, for times that may be
of the order of $\eps^{1}$, the solution stays close to
some instanton, whose center, suitably normalized, converges to a
Brownian motion plus a drift. This drift is known to be
zero in the symmetric case, and, using a perturbative
analysis, we show that, if the nonsymmetric part
of the reaction term is sufficiently small,
it determines the sign of the drift.
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