  The real Ginzburg-Landau equation possesses a family of spatially periodic
equilibria. If the wave number of an equilibrium is strictly below the so
called Eckhaus boundary the equilibrium is known to be spectrally and
diffusively stable, i.e., stable w.r.t. small spatially localized
perturbations. If the wave number is above the Eckhaus boundary the equilibrium
is unstable. Exactly at the boundary spectral stability holds. The purpose of
the present paper is to establish the diffusive stability of these equilibria.
The limit profile is determined by a nonlinear equation since a nonlinear term
turns out to be marginal w.r.t. the linearized dynamics.
