Sufficient conditions are given for existence and uniqueness in Smoluchowski's coagulation equation, for a wide class of coagulation kernels and initial mass distributions. An example of nonuniqueness is constructed. The stochastic coalescent is shown to converge weakly to the solution of Smoluchowski's equation.
"Smoluchowski's coagulation equation: uniqueness, nonuniqueness and a hydrodynamic limit for the stochastic coalescent." Ann. Appl. Probab. 9 (1) 78 - 109, February 1999. https://doi.org/10.1214/aoap/1029962598