Smoluchowski's coagulation equation : probabilistic interpretation of solutions for constant, additive and multiplicative kernels

 Access to full text

 Full (PDF)

1. [Ald99] D.J. Aldous, Deterministic and Stochastic Models for Coalescence (Aggregation, Coagulation): A Review of the Mean-Field Theory for Probabilists, Bernoulli5 (1999), 3-48. Zbl0930.60096MR1673235
2. [AN72] K.B. Athreya - P.E. Ney, "Branching Processes", Springer, 1972. Zbl0259.60002MR373040
3. [Bab99] H. Babovsky, On a Monte Carlo scheme for Smoluchowski's coagulation equation, Monte Carlo Methods Appl.5 (1999), 1-18. Zbl0937.76058MR1684990
4. [BC90] J.M. Ball - J. Carr, The discrete coagulation-fragmentation equations: existence, uniqueness and density conservation, J. Stat. Phys.61 (1990), 203-234. Zbl1217.82050MR1084278
5. [CdC92] J. Carr - F.P. Da Costa, Instantaneous gelation in coagulation dynamics, Z. Angew. Math. Phys.43 (1992), 974-983. Zbl0761.76011MR1198671
6. [Dra72] R. Drake, "A general mathematical survey of the coagulation equation", vol. 3, Pergamon Press, Oxford, 1972, 201-376. 
7. [Dub94] P.B. Dubovskii, "Mathematical theory of coagulation", Global Analysis Research Center, Seoul National University, vol. 23, 1994. Zbl0880.35124MR1290321
8. [EP98] S.N. Evans - J. Pitman, Construction of Markovian coalescents, Ann. Inst. H. Poincaré Probab. Statis.34 (1998), 339-383. Zbl0906.60058MR1625867
9. [EZH84] M.H. Ernst - R.M. Ziff - E.M. Hendriks, Coagulation Processes with phase transition, J. Colloid Interface Sci.97 (1984), 266-277. 
10. [Fe166] W. Feller, "An Introduction to Probability Theory and Its Applications", John Wiley and Sons, 1966. Zbl0155.23101MR210154
11. [Flo41a] P.J. Flory, Molecular size distribution in three dimensional polymers. I. Gelation, J. Amer. Chem. Soc.63 (1941), 3091-3096. 
12. [Flo41b] P.J. Flory, Molecular size distribution in three dimensional polymers. II. Trifunctional branching units, J. Amer. Chem. Soc.63 (1941), 3083-3090. 
13. [Flo41c] P.J. Flory, Molecular size distribution in three dimensional polymers. III. Tetrafunctional branching units, J. Amer. Chem. Soc.63 (1941), 3096-3100. 
14. [Gol63] A.M. Golovin, The solution of the coagulating equation for cloud droplets in a rising air current, Izv. Geophys. 5 (1963), 482-487. 
15. [Gor62] M. Gordon, Good's theory of cascade processes applied to the statistics of polymer distribution, Proc. Royal Soc. London Ser. A268 (1962), 240-259. 
16. [Gui98] F. Guias, Coagulation-fragmentation processes : relations between finite particle models and differential equations, PhD thesis, Universitat Heidelberg, 1998. Zbl0909.34040
17. [Hei92] O.J. Heilmann, Analytical solutions of Smoluchowski's coagulation equation, J. Phys.A25 (1992), 3763-3771. Zbl0754.92023MR1172075
18. [Jeo98] I. Jeon, Existence of gelling solutions for coagulation-fragmentation equations, Comm. Math. Phys. 194 (1998), 541-567. Zbl0910.60083MR1631473
19. [Kok88] N.J. Kokholm, On Smoluchowski's coagulation equation, J. Phys. A21 (1988), 839-842. Zbl0649.34007MR930840
20. [Lau99] P. Laurencot, The discrete coagulation equations : existence of solutions and gelation, Private Communication, 1999. 
21. [Ley84] F. Leyvraz, Phys. Rev.A29 (1984), 854. 
22. [LN80] R. Lang - X.X. Nguyen, Smoluchowski's theory of coagulation in colloids holds rigorously in the Boltzmann-Grad-Limit, Z. Wahrscheinlichkeitstheorie verw. Gebiete54 (1980), 227-280. Zbl0449.60074MR602510
23. [LT81] F. Leyvraz - H.R. Tschudi, Singularities in the kinetics of coagulation processes, J. Phys. A: Math. Gen.14 (1981), 3389-3405. Zbl0481.92020MR639565
24. [Mc62] J.B. Mcleod, On an infinite set of non-linear differential equations, Quart. J. Math. Oxford Ser. (2), 13 (1962), 119-128. Zbl0109.31501MR139822
25. [Mel57] Z.A. Melzak, A scalar transport equation, Trans. Amer. Math. Soc. 85 (1957), 547-560. Zbl0077.30505MR87880
26. [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. Zbl0944.60082MR1682596
27. [Smo16] M.V. Smoluchowski, Drei Vortage uber Diffusion, Brownsche Bewegung und Koagulation von Kolloidteilchen, Physik17 (1916), 557-585. 
28. [Spo83a] J.L. Spouge, Asymmetric bonding of identical units: a general AgRBf-g polymer model, Macromolecules16 (1983), 831-835. 
29. [Spo83b] J.L. Spouge, Equilibrium polymer distributions, Macromolecules16 (1983), 121-127. 
30. [Spo83c] J.L. Spouge, The size distribution for the Ag RB f-g model of polymerization, J. Stat. Phys.31 (1983), 363-378. MR711483
31. [Spo84] J.L. Spouge, A branching-process solution of the polydisperse coagulation equation, Adv. Appl. Prob.16 (1984), 56-69. Zbl0528.60083MR732130
32. [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. MR811992

1. Jean Bertoin, Two solvable systems of coagulation equations with limited aggregations
2. M. Escobedo, S. Mischler, M. Rodriguez Ricard, On self-similarity and stationary problem for fragmentation and coagulation models