We construct a time-dependent solution to the Smoluchowski coagulation
equation with a constant flux of dust particles entering through the
boundary at zero. The dust is instantaneously converted into particles
of positive size; as a result, flux solutions have linearly increasing
mass. Flux solutions are expected to approximate the large size
behaviour of solutions of coagulation equations with source. The
construction is made for a general class of non-gelling coagulation
kernels for which non-trivial stationary solutions do exist. In the
complementary regimes, including for gelling kernels, such flux
solutions with finite mass cannot exist. Flux solutions are expected to
converge to a stationary solution in the large time limit. We show that
this is indeed true in the particular case of the constant kernel with
zero initial data. (Based on a joint work with Aleksis Vuoksenmaa - U.
Helsinki)