Non-equilibrium Stationary Solutions for Multicomponent Coagulation Systems with Injection

The existence and non-existence of stationary solutions of multicomponent coagulation equations with a constant flux of mass towards large sizes is investigated. The flux may be induced by a source of small clusters or by a flux boundary condition at the origin of the composition space, and the coagulation kernel can be very general, merely satisfying certain power law asymptotic bounds in terms of the total number of monomers in a cluster. Our set-up, including an appropriate definition of multicomponent flux, allows a sharp classification of the existence of stationary solutions. In particular, this analysis extends previous results for one-component systems to a larger class of kernels.