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The Smoluchowski coagulation equation is a coupled system of partial differential equations that describes the evolving densities of a system of diffusing particles that are prone to coagulate in pairs. Under some natural conditions on the collision propensities and the diffusion rates, one obtains various bounds on the moments of the densities. As a consequence, we infer that these conditions are sufficient to ensure uniqueness of a weak solution and its conservation of mass. (This is a joint work with Alan Hammond.)

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