Self-similar behaviour in the coagulation equations

Davies, S.C.; King, J. R. and Wattis, J. A. D. (1999). Self-similar behaviour in the coagulation equations. Journal of Engineering Mathematics, 36 pp. 57–88.

DOI: https://doi.org/10.1023/A:1004589822425

Abstract

This paper describes solutions to the Smoluchowski coagulation equations with power-law kernels in both constant-mass and constant-monomer cases. Exact solutions are obtained in special cases by a generating function approach. For more general kernels, the large-time behaviour is obtained by use of matched asymptotics. Numerical results are also given, which confirm the asymptotic analysis.

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