Communications in Mathematical Sciences

Volume 2 (2004)

Supp. 1

Supplemental Issue 1

Uniqueness via probabilistic interpretation for the discrete coagulation fragmentation equation

Pages: 75 – 83



Benjamin Jourdain (ENPC-CERMICS, Marne-la-Vallée, France)


In this paper, supposing that either the initial data is small or the fragmentation phenomenon dominates the coagulation, we associate a nonlinear stochastic process with any solution of the mass-flow equation obtained from the discrete Smoluchowski coagulation fragmentation equation by a natural change of variables. This enables us to deduce uniqueness for the mass flow equation and therefore for the corresponding Smoluchowski equation thanks to a coupling argument.

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