On the Evolution of Large Clusters in the Becker-D?ring Model

Summary. We consider the Becker-D?ring equations for large times. It is well-known 2] that if the total density of monomers exceeds a critical value, the excess density is contained in larger and larger clusters as time proceeds. We rigorously derive for general coefficients that the evolution of these large clusters is described by a nonlocal transport equation, which is for specific coefficients the classical coarsening model by Lifshitz, Slyozov, and Wagner (LSW). Our proof exploits the estimate of the energy and the energy dissipation rate given by the Lyapunov functional for the Becker-D?ring equations. We also provide a detailed asymptotic expansion of the higher-order dynamics.