  We study the effect of fluctuations in the vicinity of an Eckhaus
instability. The classical stability limit, which is defined in the absence of
fluctuations, is smeared out into a region in which fluctuations and
nonlinearities dominate the decay of unstable states. The width of this region
is shown to grow as $ D^{1/2} $, where $D$ is the intensity of the
fluctuations. We find an effective stability boundary that depends on $D$. A
numerical solution of the stochastic Swift-Hohenberg equation in one dimension
is used to test this prediction and to study pattern selection when the initial
unstable state lies within the fluctuation dominated region. The asymptotically
selected state differs from the predictions of previous analyses. Finally, the
nonlinear relaxation for $D > 0$ is shown to exhibit a scaling form.

Condensed Matter;Pattern Formation and Solitons;Pattern Formation and Solitons