Uniqueness of post-gelation solutions of a class of coagulation equations
Annales de l'I.H.P. Analyse non linéaire, Volume 28 (2011) no. 2, p. 189-215
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.
DOI : https://doi.org/10.1016/j.anihpc.2010.10.005
Classification:  34A34,  82D60
Keywords: Coagulation equations, Gelation, Generating functions, Method of characteristics, Long-time behavior
@article{AIHPC_2011__28_2_189_0,
author = {Normand, Raoul and Zambotti, Lorenzo},
title = {Uniqueness of post-gelation solutions of a class of coagulation equations},
journal = {Annales de l'I.H.P. Analyse non lin\'eaire},
publisher = {Elsevier},
volume = {28},
number = {2},
year = {2011},
pages = {189-215},
doi = {10.1016/j.anihpc.2010.10.005},
zbl = {1213.82116},
mrnumber = {2784069},
language = {en},
url = {http://www.numdam.org/item/AIHPC_2011__28_2_189_0}
}

Normand, Raoul; Zambotti, Lorenzo. Uniqueness of post-gelation solutions of a class of coagulation equations. Annales de l'I.H.P. Analyse non linéaire, Volume 28 (2011) no. 2, pp. 189-215. doi : 10.1016/j.anihpc.2010.10.005. http://www.numdam.org/item/AIHPC_2011__28_2_189_0/

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