The Becker–Döring Model with Diffusion II. Long Time Behavior

Long time behaviour of solutions to the Becker–Döring model with diffusion is investigated. Under general assumptions on the diffusion coefficients, it is shown that theω-limit sets of the solutions in a suitable topology only contain spatially homogeneous steady states. Theseω-limit sets are then proved to be reduced to a single element, provided that the diffusion coefficients do not decay too fast to zero.