  We investigate a spatially flat Friedmann-Lema\^itre-Robertson-Walker
cosmology in which a decaying vacuum term causes matter production at late
times. Assuming a decay proportional to the Hubble rate, the ratio of the
background energy densities of dark matter and dark energy changes with the
cosmic scale factor as $a^{-3/2}$. The intrinsically non-adiabatic
two-component perturbation dynamics of this model is reduced to a single
second-order equation. Perturbations of the vacuum term are shown to be
negligible on scales that are relevant for structure formation. On larger
scales, dark-energy perturbations give a somewhat higher contribution but
remain always smaller than the dark-matter perturbations.
