Rates of convergence for Smoluchowski's coagulation equations

Abstract

We establish nearly optimal rates of convergence to self-similar solutions of Smoluchowski's coagulation equation with kernels $K = 2$, $x + y$, and $xy$. The method is a simple analogue of the Berry-Ess\'een theorem in classical probability and requires minimal assumptions on the initial data, namely that of an extra finite moment condition. For each kernel it is shown that the convergence rate is achieved in the case of monodisperse initial data.