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This article is devoted to a generalized version of Smoluchowski'scoagulation equation. This model describes the time evolution of a system ofaggregating particles under the effect of external input and output particles.We show that for a large class of coagulation kernels, output rates, andexponentially decaying input rates, there is a weak solution. Moreover, thesolution satisfies the mass-conservation property for linear coagulation rateand an additional condition on input and output rates. The uniqueness of weaksolutions is also established by applying additional restrictions on the rates.

Existence and uniqueness of weak solutions to the Smoluchowski coagulation equation with source and sedimentation