The kinetics of the Ostwald ripening in a homogeneous supersaturated solution is studied both numerically and analytically. The time evolution of the grain-size distribution function in a new phase is theoretically described, taking into account the finite value of the maximal size of a grain. Two situations are considered: the kinetics of grain growth is controlled either by the grain-monomer reaction process (an early stage) or by the monomer diffusion process (a late stage). A transition to the final distribution is shown to take place through an intermediate-asymptotical mode of the Ostwald ripening kinetics, the crossover of the kinetic indices is demonstrated, and the duration of intermediate stage is evaluated.
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