  We present a model for studying the formation and evaporation of non-singular
(quantum corrected) black holes. The model is based on a generalized form of
the dimensionally reduced, spherically symmetric Einstein--Hilbert action and
includes a suitably generalized Polyakov action to provide a mechanism for
radiation back-reaction. The equations of motion describing self-gravitating
scalar field collapse are derived in local form both in null co--ordinates and
in Painleve--Gullstrand (flat slice) co--ordinates. They provide the starting
point for numerical studies of complete spacetimes containing dynamical
horizons that bound a compact trapped region. Such spacetimes have been
proposed in the past as solutions to the information loss problem because they
possess neither an event horizon nor a singularity. Since the equations of
motion in our model are derived from a diffeomorphism invariant action they
preserve the constraint algebra and the resulting energy momentum tensor is
manifestly conserved.
