Smoluchowski's coagulation equation: uniqueness, non-uniqueness and a hydrodynamic limit for the stochastic coalescent

1998/01/09 by James R. Norris, Norris, James R. · 2 citations
Mathematics · Physics and Astronomy · #Advanced Thermodynamics and Statistical Mechanics #Mathematical Biology Tumor Growth #math.PR #stochastic dynamics and bifurcation

paper · pdf · doi:10.48550/arxiv.math/9801145

arxiv created 1998/01/09 · arxiv updated 2009/11/30

Abstract

Sufficient conditions are given for existence and uniqueness in Smoluchowski's coagulation equation, for a wide class of coagulation kernels and initial mass distributions. An example of non-uniqueness is constructed. The stochastic coalescent is shown to converge weakly to the solution of Smoluchowski's equation.

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• Existence and Non-existence for Continuous Generalized Exchange-Driven Growth model
• Marcus-Lushnikov processes, Smoluchowski's and Flory's models

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