Rates of Convergence for Smoluchowski's Coagulation Equations

Ravi Srinivasan

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–Esséen 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.