  The Davies-Fulling (DF) model describes the scattering of a massless field by
a non-inertial mirror in two dimensions. In this paper, we generalize this
model in two different ways. First, we consider partially reflecting mirrors.
We show that the Bogoliubov coefficients relating inertial modes can be
expressed in terms of the frequency dependent reflection factor which is
specified in the rest frame of the mirror and the transformation from the
inertial modes to the modes at rest with respect to the mirror. In this
perspective, the DF model is simply the limiting case when this factor is unity
for all frequencies. In the second part, we introduce an alternative model
which is based on self-interactions described by an action principle. When the
coupling is constant, this model can be solved exactly and gives rise to a
partially reflecting mirror. The usefulness of this dynamical model lies in the
possibility of switching off the coupling between the mirror and the field.
This allows to obtain regularized expressions for the fluxes in situations
where they are singular when using the DF model. Two examples are considered.
The first concerns the flux induced by the disappearance of the reflection
condition, a situation which bears some analogies with the end of the
evaporation of a black hole. The second case concerns the flux emitted by a
uniformly accelerated mirror.
