Summary
We consider Smoluchowski's model of coagulation in colloids: n particles move in three-dimensional euclidean space according to Brownian motions independently of each other as long as the particles are at a distance greater than R. When two particles come to within a distance R they stick together and form a “double particle”, which itself is in Brownian motion — and so on. In the Boltzmann-Grad-limit n→∞, n R=constant, we prove “propagation of chaos” and derive the kinetic equations for the densities of the k-fold particles.
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Research supported by the Deutsche Forschungsgemeinschaft (Sonderforschungsbereich 123)
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Lang, R., Xanh, N.X. Smoluchowski's theory of coagulation in colloids holds rigorously in the Boltzmann-Grad-limit. Z. Wahrscheinlichkeitstheorie verw Gebiete 54, 227–280 (1980). https://doi.org/10.1007/BF00534345
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DOI: https://doi.org/10.1007/BF00534345