BROWNIAN COAGULATION AND A VERSION OF SMOLUCHOWSKI'S EQUATION ON THE CIRCLE

• 成果类型: Article
• 署名作者: Armendariz, Ines
• 刊物名称: ANNALS OF APPLIED PROBABILITY
• ISSN/ISSBN: 1050-5164
• DOI: 10.1214/09-AAP633
• 发表日期: 2010
• 页码: 660-695
• 关键词: kinetic limit; SYSTEM

摘要

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.