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.
Cite this article
Raoul Normand, Lorenzo Zambotti, Uniqueness of post-gelation solutions of a class of coagulation equations. Ann. Inst. H. Poincaré Anal. Non Linéaire 28 (2011), no. 2, pp. 189–215DOI 10.1016/J.ANIHPC.2010.10.005