On existence of steady-state solutions to the coagulation equations

The general steady-state coagulation equations with sources and sinks are examined. These equations are shown to admit physically unacceptable solutions in some cases, and it is hypothesized that in such a case a gelation or precipitation phenomenon occurs. General conditions on the coagulation and loss coefficients are given that insure the existence of physically realistic solutions. The physically realistic solutions have tails that decay faster than any power of particle size.