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.
Mots-clés : 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}, pages = {189--215}, publisher = {Elsevier}, volume = {28}, number = {2}, year = {2011}, doi = {10.1016/j.anihpc.2010.10.005}, mrnumber = {2784069}, zbl = {1213.82116}, language = {en}, url = {http://www.numdam.org/articles/10.1016/j.anihpc.2010.10.005/} }
TY - JOUR AU - Normand, Raoul AU - Zambotti, Lorenzo TI - Uniqueness of post-gelation solutions of a class of coagulation equations JO - Annales de l'I.H.P. Analyse non linéaire PY - 2011 SP - 189 EP - 215 VL - 28 IS - 2 PB - Elsevier UR - http://www.numdam.org/articles/10.1016/j.anihpc.2010.10.005/ DO - 10.1016/j.anihpc.2010.10.005 LA - en ID - AIHPC_2011__28_2_189_0 ER -
%0 Journal Article %A Normand, Raoul %A Zambotti, Lorenzo %T Uniqueness of post-gelation solutions of a class of coagulation equations %J Annales de l'I.H.P. Analyse non linéaire %D 2011 %P 189-215 %V 28 %N 2 %I Elsevier %U http://www.numdam.org/articles/10.1016/j.anihpc.2010.10.005/ %R 10.1016/j.anihpc.2010.10.005 %G en %F 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, Tome 28 (2011) no. 2, pp. 189-215. doi : 10.1016/j.anihpc.2010.10.005. http://www.numdam.org/articles/10.1016/j.anihpc.2010.10.005/
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