Abstract
We consider the connection between two mean-field models describing the binary coagulation of discrete clusters moving by spatial diffusion. Both models are generalizations of Smoluchowski's infinite system of coagulation equations. In the first (local) model, the coagulation rates are proportional to the concentrations of the interacting clusters as a consequence of the assumption that two clusters coalesce only if they meet at the same point. In the second (nonlocal) one, the coagulation rates contain integral terms which reflect the nonlocal character of interactions between clusters, the intensity of clusters' encounters depending on the distance between them and being measured by means of some positive parameter ε. It is proved that weak solutions to the nonlocal discrete diffusive coagulation equations converge to that of the local one as ε → 0.
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