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

Abstract

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 ${\rho }_s$ such that solutions with an initial density ${\rho }_0\le {\rho }_s$ converge strongly to the equilibrium with density ${\rho }_0$, and solutions with initial density ${\rho }_0>{\rho }_s$ converge (in a weak sense) to the equilibrium with density ${\rho }_s$. 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.

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