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arXiv · 1009.5747

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

Inés Armendáriz
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Abstract

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

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Inés Armendáriz. 2010-09-28. Brownian coagulation and a version of Smoluchowski's equation on the circle. https://doi.org/10.1214/09-aap633

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