Weak selection and stability of localized distributions in Ostwald ripening

We support and generalize a weak selection rule predicted recently for the self-similar asymptotics of the distribution function (DF) in the zero-volume-fraction limit of Ostwald ripening (OR). An asymptotic perturbation theory is developed that, when combined with an exact invariance property of the system, yields the selection rule in terms of the initial condition, predicts a power-law convergence towards the selected self-similar DF, and agrees well with our numerical simulations for the interface- and diffusion-controlled OR.