JournalsaihpcVol. 28, No. 2pp. 189–215

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

  • Raoul Normand

    Laboratoire de Probabilités et Modèles Aléatoires, Université Paris 6 – Pierre et Marie Curie, 175 rue du Chevaleret, 75013 Paris, France

  • Lorenzo Zambotti

    Laboratoire de Probabilités et Modèles Aléatoires, Université Paris 6 – Pierre et Marie Curie, 175 rue du Chevaleret, 75013 Paris, France
Uniqueness of post-gelation solutions of a class of coagulation equations cover
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Abstract

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. 189–215

DOI 10.1016/J.ANIHPC.2010.10.005