Asymptotic behavior of the generalized Becker-Döring equations for general initial data

We prove the following asymptotic behavior for solutions to the generalized Becker-Döring system for general initial data: under a detailed balance assumption and in situations where density is conserved in time, there is a critical density rhos such that solutions with an initial density rho0 leq rhos converge strongly to the equilibrium with density rho0, and solutions with initial density rho0 > rhos converge (in a weak sense) to the equilibrium with density rhos. This extends the previous knowledge that this behavior happens under more restrictive conditions on the initial data. The main tool is a new estimate on the tail of solutions with density below the critical density.