  We consider a stochastically perturbed reaction diffusion equation in a
bounded interval, with boundary conditions imposing the two stable phases at
the endpoints. We investigate the asymptotic behavior of the front separating
the two stable phases, as the intensity of the noise vanishes and the size of
the interval diverges. In particular, we prove that, in a suitable scaling
limit, the front evolves according to a one-dimensional diffusion process with
a non-linear drift accounting for a "soft" repulsion from the boundary. We
finally show how a "hard" repulsion can be obtained by an extra diffusive
scaling.
