  In this article we study an extension of Smoluchowski's discrete coagulation
equation, where particle in- and output takes place. This model is frequently
used to describe aggregation processes in combination with sedimentation of
clusters. More precisely, we show that the evolution equation is well-posed for
a large class of coagulation kernels and output rates. Additionally, in the
long-time limit we prove that solutions converge to a unique equilibrium with
exponential rate under a suitable smallness condition on the coefficients.
