Two Solvable Systems of Coagulation Equations With Limited Aggregations
Annales de l'I.H.P. Analyse non linéaire, Volume 26 (2009) no. 6, pp. 2073-2089.
@article{AIHPC_2009__26_6_2073_0,
     author = {Bertoin, Jean},
     title = {Two {Solvable} {Systems} of {Coagulation} {Equations} {With} {Limited} {Aggregations}},
     journal = {Annales de l'I.H.P. Analyse non lin\'eaire},
     pages = {2073--2089},
     publisher = {Elsevier},
     volume = {26},
     number = {6},
     year = {2009},
     doi = {10.1016/j.anihpc.2008.10.007},
     zbl = {1179.82180},
     mrnumber = {2569886},
     language = {en},
     url = {http://archive.numdam.org/articles/10.1016/j.anihpc.2008.10.007/}
}
TY  - JOUR
AU  - Bertoin, Jean
TI  - Two Solvable Systems of Coagulation Equations With Limited Aggregations
JO  - Annales de l'I.H.P. Analyse non linéaire
PY  - 2009
DA  - 2009///
SP  - 2073
EP  - 2089
VL  - 26
IS  - 6
PB  - Elsevier
UR  - http://archive.numdam.org/articles/10.1016/j.anihpc.2008.10.007/
UR  - https://zbmath.org/?q=an%3A1179.82180
UR  - https://www.ams.org/mathscinet-getitem?mr=2569886
UR  - https://doi.org/10.1016/j.anihpc.2008.10.007
DO  - 10.1016/j.anihpc.2008.10.007
LA  - en
ID  - AIHPC_2009__26_6_2073_0
ER  - 
%0 Journal Article
%A Bertoin, Jean
%T Two Solvable Systems of Coagulation Equations With Limited Aggregations
%J Annales de l'I.H.P. Analyse non linéaire
%D 2009
%P 2073-2089
%V 26
%N 6
%I Elsevier
%U https://doi.org/10.1016/j.anihpc.2008.10.007
%R 10.1016/j.anihpc.2008.10.007
%G en
%F AIHPC_2009__26_6_2073_0
Bertoin, Jean. Two Solvable Systems of Coagulation Equations With Limited Aggregations. Annales de l'I.H.P. Analyse non linéaire, Volume 26 (2009) no. 6, pp. 2073-2089. doi : 10.1016/j.anihpc.2008.10.007. http://archive.numdam.org/articles/10.1016/j.anihpc.2008.10.007/

[1] Aldous D. J., Deterministic and Stochastic Models for Coalescence (Aggregation, Coagulation): a Review of the Mean-Field Theory for Probabilists, Bernoulli 5 (1999) 3-48. | MR | Zbl

[2] Bertoin J., Sidoravicius V., The Structure of Typical Clusters in Large Sparse Random Configurations, available at, http://hal.archives-ouvertes.fr/ccsd-00339779/en/. | Zbl

[3] Bertoin J., Sidoravicius V., Vares M. E., A System of Grabbing Particles Related to Galton-Watson Trees, Preprint available at, http://fr.arXiv.org/abs/0804.0726.

[4] Billingsley P., Probability and Measure, third ed., John Wiley & Sons, New York, 1995. | MR | Zbl

[5] Deaconu M., Tanré E., Smoluchovski's Coagulation Equation: Probabilistic Interpretation of Solutions for Constant, Additive and Multiplicative Kernels, Ann. Scuola Normale Sup. Pisa XXIX (2000) 549-580. | Numdam | MR | Zbl

[6] Drake R. L., A General Mathematical Survey of the Coagulation Equation, in: Hidy G. M., Brock J. R. (Eds.), Topics in Current Aerosol Research, Part 2, International Reviews in Aerosol Physics and Chemistry, Pergamon Press, Oxford, 1972, pp. 201-376.

[7] Dubovski P. B., Mathematical Theory of Coagulation, Seoul National University, Seoul, 1994. | MR | Zbl

[8] Dwass M., The Total Progeny in a Branching Process and a Related Random Walk, J. Appl. Probab. 6 (1969) 682-686. | MR | Zbl

[9] Escobedo M., Mischler S., Dust and Self-Similarity for the Smoluchowski Coagulation Equation, Ann. Inst. H. Poincaré Anal. Non Linéaire 23 (2006) 331-362. | Numdam | MR | Zbl

[10] Fournier N., Laurençot Ph., Existence of Self-Similar Solutions to Smoluchowski's Coagulation Equation, Comm. Math. Phys. 256 (2005) 589-609. | MR | Zbl

[11] Golovin A. M., The Solution of the Coagulation Equation for Cloud Droplets in a Rising Air Current, Izv. Geophys. Ser. 5 (1963) 482-487.

[12] Jeon I., Existence of Gelling Solutions for Coagulation-Fragmentation Equations, Comm. Math. Phys. 194 (1998) 541-567. | MR | Zbl

[13] Laurençot Ph., Mischler S., On Coalescence Equations and Related Models, in: Degond P., Pareschi L., Russo G. (Eds.), Modeling and Computational Methods for Kinetic Equations, Birkhäuser, 2004, pp. 321-356. | MR | Zbl

[14] Mcleod J. B., On an Infinite Set of Nonlinear Differential Equations, Quart. J. Math. Oxford 13 (1962) 119-128. | MR | Zbl

[15] Menon G., Pego R. L., Approach to Self-Similarity in Smoluchowski's Coagulation Equations, Comm. Pure Appl. Math. 57 (2004) 1197-1232. | MR | Zbl

[16] Norris J. R., Cluster Coagulation, Comm. Math. Phys. 209 (2000) 407-435. | MR | Zbl

[17] Von Smoluchowski M., Drei Vortrage Über Diffusion, Brownsche Molekularbewegung Und Koagulation Von Kolloidteilchen, Phys. Z. 17 (1916) 557-571, and 585-599.

[18] Spouge J. L., Solutions and Critical Times for the Monodisperse Coagulation Equation When a(x,y)=A+B(x+y)+Cxy, J. Phys. A: Math. Gen. 16 (1983) 767-773. | MR | Zbl

[19] Spouge J. L., A Branching-Process Solution of the Polydisperse Coagulation Equation, Adv. Appl. Probab. 16 (1984) 56-69. | MR | Zbl

[20] Trubnikov B., Solution of the Coagulation Equation in the Case of a Bilinear Coefficient of Adhesion of Particles, Soviet Phys. Dokl. 16 (1971) 124-125.

[21] Van Dongen P. G.J., Ernst M. H., Size Distribution in the Polymerization Model A f RB g , J. Phys. A: Math. Gen. 17 (1984) 2281-2297. | MR

[22] Van Dongen P. G.J., Ernst M. H., On the Occurrence of a Gelation Transition in Smoluchowski's Coagulation Equation, J. Statist. Phys. 44 (1986) 785-792. | MR

[23] Wilf H. S., Generatingfunctionology, Academic Press, 1994, Also available via, http://www.math.upenn.edu/~wilf/gfology2.pdf. | MR | Zbl

Cited by Sources: