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We introduce a one-dimensional stochastic system where particles performindependent diffusions and interact through pairwise coagulation events, whichoccur at a nontrivial rate upon collision. Under appropriate conditions on thediffusion coefficients, the coagulation rates and the initial distribution ofparticles, we derive a spatially inhomogeneous version of the mass flowequation as the particle number tends to infinity. The mass flow equation is inone-to-one correspondence with Smoluchowski's coagulation equation. We proveuniqueness for this equation in a broad class of solutions, to which the weaklimit of the stochastic system is shown to belong.

Brownian coagulation and a version of Smoluchowski's equation on the circle