  We study coagulation equations under non-equilibrium conditions which are
induced by the addition of a source term for small cluster sizes. We consider
both discrete and continuous coagulation equations, and allow for a large class
of coagulation rate kernels, with the main restriction being boundedness from
above and below by certain weight functions. The weight functions depend on two
power law parameters, and the assumptions cover, in particular, the commonly
used free molecular and diffusion limited aggregation coagulation kernels. Our
main result shows that the two weight function parameters already determine
whether there exists a stationary solution under the presence of a source term.
In particular, we find that the diffusive kernel allows for the existence of
stationary solutions while there cannot be any such solutions for the free
molecular kernel. The argument to prove the non-existence of solutions relies
on a novel power law lower bound, valid in the appropriate parameter regime,
for the decay of stationary solutions with a constant flux. We obtain optimal
lower and upper estimates of the solutions for large cluster sizes, and prove
that the solutions of the discrete model behave asymptotically as solutions of
the continuous model.
