Stationary Non-equilibrium Solutions for Coagulation Systems

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