Smoluchowski's coagulation equation : probabilistic interpretation of solutions for constant, additive and multiplicative kernels
Annali della Scuola Normale Superiore di Pisa - Classe di Scienze, Série 4, Volume 29 (2000) no. 3, p. 549-579
@article{ASNSP_2000_4_29_3_549_0,
     author = {Deaconu, Madalina and Tanr\'e, Etienne},
     title = {Smoluchowski's coagulation equation : probabilistic interpretation of solutions for constant, additive and multiplicative kernels},
     journal = {Annali della Scuola Normale Superiore di Pisa - Classe di Scienze},
     publisher = {Scuola normale superiore},
     volume = {Ser. 4, 29},
     number = {3},
     year = {2000},
     pages = {549-579},
     zbl = {1072.60071},
     mrnumber = {1817709},
     language = {en},
     url = {http://www.numdam.org/item/ASNSP_2000_4_29_3_549_0}
}
Deaconu, Madalina; Tanré, Etienne. Smoluchowski's coagulation equation : probabilistic interpretation of solutions for constant, additive and multiplicative kernels. Annali della Scuola Normale Superiore di Pisa - Classe di Scienze, Série 4, Volume 29 (2000) no. 3, pp. 549-579. http://www.numdam.org/item/ASNSP_2000_4_29_3_549_0/

[Ald99] D.J. Aldous, Deterministic and Stochastic Models for Coalescence (Aggregation, Coagulation): A Review of the Mean-Field Theory for Probabilists, Bernoulli 5 (1999), 3-48. | MR 1673235 | Zbl 0930.60096

[AN72] K.B. Athreya - P.E. Ney, "Branching Processes", Springer, 1972. | MR 373040 | Zbl 0259.60002

[Bab99] H. Babovsky, On a Monte Carlo scheme for Smoluchowski's coagulation equation, Monte Carlo Methods Appl. 5 (1999), 1-18. | MR 1684990 | Zbl 0937.76058

[BC90] J.M. Ball - J. Carr, The discrete coagulation-fragmentation equations: existence, uniqueness and density conservation, J. Stat. Phys. 61 (1990), 203-234. | MR 1084278

[CdC92] J. Carr - F.P. Da Costa, Instantaneous gelation in coagulation dynamics, Z. Angew. Math. Phys. 43 (1992), 974-983. | MR 1198671 | Zbl 0761.76011

[Dra72] R. Drake, "A general mathematical survey of the coagulation equation", vol. 3, Pergamon Press, Oxford, 1972, 201-376.

[Dub94] P.B. Dubovskii, "Mathematical theory of coagulation", Global Analysis Research Center, Seoul National University, vol. 23, 1994. | MR 1290321 | Zbl 0880.35124

[EP98] S.N. Evans - J. Pitman, Construction of Markovian coalescents, Ann. Inst. H. Poincaré Probab. Statis. 34 (1998), 339-383. | Numdam | MR 1625867 | Zbl 0906.60058

[EZH84] M.H. Ernst - R.M. Ziff - E.M. Hendriks, Coagulation Processes with phase transition, J. Colloid Interface Sci. 97 (1984), 266-277.

[Fe166] W. Feller, "An Introduction to Probability Theory and Its Applications", John Wiley and Sons, 1966. | MR 210154 | Zbl 0155.23101

[Flo41a] P.J. Flory, Molecular size distribution in three dimensional polymers. I. Gelation, J. Amer. Chem. Soc. 63 (1941), 3091-3096.

[Flo41b] P.J. Flory, Molecular size distribution in three dimensional polymers. II. Trifunctional branching units, J. Amer. Chem. Soc. 63 (1941), 3083-3090.

[Flo41c] P.J. Flory, Molecular size distribution in three dimensional polymers. III. Tetrafunctional branching units, J. Amer. Chem. Soc. 63 (1941), 3096-3100.

[Gol63] A.M. Golovin, The solution of the coagulating equation for cloud droplets in a rising air current, Izv. Geophys. 5 (1963), 482-487.

[Gor62] M. Gordon, Good's theory of cascade processes applied to the statistics of polymer distribution, Proc. Royal Soc. London Ser. A 268 (1962), 240-259.

[Gui98] F. Guias, Coagulation-fragmentation processes : relations between finite particle models and differential equations, PhD thesis, Universitat Heidelberg, 1998. | Zbl 0909.34040

[Hei92] O.J. Heilmann, Analytical solutions of Smoluchowski's coagulation equation, J. Phys. A 25 (1992), 3763-3771. | MR 1172075 | Zbl 0754.92023

[Jeo98] I. Jeon, Existence of gelling solutions for coagulation-fragmentation equations, Comm. Math. Phys. 194 (1998), 541-567. | MR 1631473 | Zbl 0910.60083

[Kok88] N.J. Kokholm, On Smoluchowski's coagulation equation, J. Phys. A 21 (1988), 839-842. | MR 930840 | Zbl 0649.34007

[Lau99] P. Laurencot, The discrete coagulation equations : existence of solutions and gelation, Private Communication, 1999.

[Ley84] F. Leyvraz, Phys. Rev. A 29 (1984), 854.

[LN80] R. Lang - X.X. Nguyen, Smoluchowski's theory of coagulation in colloids holds rigorously in the Boltzmann-Grad-Limit, Z. Wahrscheinlichkeitstheorie verw. Gebiete 54 (1980), 227-280. | MR 602510 | Zbl 0449.60074

[LT81] F. Leyvraz - H.R. Tschudi, Singularities in the kinetics of coagulation processes, J. Phys. A: Math. Gen. 14 (1981), 3389-3405. | MR 639565 | Zbl 0481.92020

[Mc62] J.B. Mcleod, On an infinite set of non-linear differential equations, Quart. J. Math. Oxford Ser. (2), 13 (1962), 119-128. | MR 139822 | Zbl 0109.31501

[Mel57] Z.A. Melzak, A scalar transport equation, Trans. Amer. Math. Soc. 85 (1957), 547-560. | MR 87880 | Zbl 0077.30505

[Nor99] J.R. Norris, Smoluchowski's coagulation equation: uniqueness, non-uniqueness and hydrodynamic limit for the stochastic coalescent, Ann. Appl. Probab. 9 (1999), 78-109. | MR 1682596 | Zbl 0944.60082

[Smo16] M.V. Smoluchowski, Drei Vortage uber Diffusion, Brownsche Bewegung und Koagulation von Kolloidteilchen, Physik 17 (1916), 557-585.

[Spo83a] J.L. Spouge, Asymmetric bonding of identical units: a general AgRBf-g polymer model, Macromolecules 16 (1983), 831-835.

[Spo83b] J.L. Spouge, Equilibrium polymer distributions, Macromolecules 16 (1983), 121-127.

[Spo83c] J.L. Spouge, The size distribution for the Ag RB f-g model of polymerization, J. Stat. Phys. 31 (1983), 363-378. | MR 711483

[Spo84] J.L. Spouge, A branching-process solution of the polydisperse coagulation equation, Adv. Appl. Prob. 16 (1984), 56-69. | MR 732130 | Zbl 0528.60083

[vDE85] P. G. J Van Dongen - M.H. Ernst, Cluster size distribution in irreversible aggregation at large times, J. Phys. A: Math. Gen. 18 (1985), 2779-2793. | MR 811992