Uniqueness of post-gelation solutions of a class of coagulation equations

Details Uniqueness of post-gelation solutions of a class of coagulation equations Uniqueness of post-gelation solutions of a class of coagulation equations

2010-02-03

arxiv.org/abs/1002.0702v3

Mathematics

Classical Analysis and ODEs

31 pages, 4 figures

Scientific paper

We prove well-posedness of global solutions for a class of coagulation equations which exhibit the gelation phase transition. To this end, we solve an associated partial differential equation involving the generating functions before and after the phase transition. Applications include the classical Smoluchowski and Flory equations with multiplicative coagulation rate and the recently introduced symmetric model with limited aggregations. For the latter, we compute the limiting concentrations and we relate them to random graph models.

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