  We prove well-posedness of the initial value problem for the Einstein
equations for spatially-homogeneous cosmologies with data at an isotropic
cosmological singularity, for which the matter content is either a cosmological
constant with collisionless particles of a single mass (possibly zero) or a
cosmological constant with a perfect fluid having the radiation equation of
state. In both cases, with a positive cosmological constant, these solutions,
except possibly for Bianchi-type-IX, will expand forever, and be
geodesically-complete into the future.
