Gelation and mass conservation in coagulation-fragmentation models

Journal of Differential Equations

Volumn 195, Issue 1, 2003, Pages 143-174

  Escobedo, M ^a   Laurencot Ph ^b   Mischler, S ^c,d   Perthame, B ^d  

^a UNIVERSITY OF THE BASQUE COUNTRY UPV EHU   (Spain)

^b INSTITUT DE MATHÉMATIQUES DE TOULOUSE   (France)

^c UNIVERSITÉ DE VERSAILLES SAINT QUENTIN EN YVELINES   (France)

^d ÉCOLE NORMALE SUPÉRIEURE   (France)

Author keywords

Coagulation; Flory's coagulation equation; Gelation; Non uniqueness; Strong fragmentation

Indexed keywords

EID: 0344981529     PISSN: 00220396     EISSN: None     Source Type: Journal    
DOI: 10.1016/S0022-0396(03)00134-7     Document Type: Article

References (26)

1. T.A. Bak, O. Heilmann, Post-gelation solutions to Smoluchowski's coagulation equation, J. Phys. A 27 (1994) 4203-4209.
2. J.M. Ball, J. Carr, The discrete coagulation-fragmentation equations: existence, uniqueness, and density conservation, J. Statist. Phys. 61 (1990) 203-234.
3. J. Banasiak, On a non-uniqueness in fragmentation models, Math. Methods Appl. Sci. 25 (2002) 541-556.
4. F.P. da Costa, Existence and uniqueness of density conserving solutions to the coagulation-fragmentation equations with strong fragmentation, J. Math. Anal. Appl. 192 (1995) 892-914.
5. C. Dellacherie, P.A. Meyer, Probabilités et Potentiel, Chapitres I à IV, Hermann, Paris, 1975.
6. R.L. Drake, A general mathematical survey of the coagulation equation, in: G.M. Hidy, J.R. Brock (Eds.), Topics in Current Aerosol Research (Part 2), International Reviews in Aerosol Physics and Chemistry, Pergamon Press, Oxford, 1972, pp. 203-376.
7. P.B. Dubovskiǐ, I.W. Stewart, Existence, uniqueness and mass conservation for the coagulation-fragmentation equation, Math. Methods Appl. Sci. 19 (1996) 571-591.
8. M.H. Ernst, R.M. Ziff, E.M. Hendriks, Coagulation processes with a phase transition, J. Colloid Interface Sci. 97 (1984) 266-277.
9. M. Escobedo, S. Mischler, B. Perthame, Gelation in coagulation and fragmentation models, Comm. Math. Phys. 231 (2002) 157-188.
10. E.M. Hendriks, M.H. Ernst, R.M. Ziff, Coagulation equations with gelation, J. Statist. Phys. 31 (1983) 519-563.
11. I. Jeon, Existence of gelling solutions for coagulation-fragmentation equations, Comm. Math. Phys. 194 (1998) 541-567.
12. Ph. Laurençot, On a class of continuous coagulation-fragmentation models, J. Differential Equations 167 (2000) 145-174.
13. Ph. Laurençot, The Lifshitz-Slyozov equation with encounters, Math. Models Methods Appl. Sci. 11 (2001) 731-748.
14. Ph. Laurençot, S. Mischler, From the discrete to the continuous coagulation-fragmentation equations, Proc. Roy. Soc. Edinburgh Sect. A 132 (2002) 1219-1248.
15. ∞ (Ω), Thèse de 3e cycle, Université de Paris VI, 1977.
16. F. Leyvraz, Existence and properties of post-gel solutions for the kinetic equations of coagulation, J. Phys. A 16 (1983) 2861-2873.
17. F. Leyvraz, H.R. Tschudi, Singularities in the kinetics of coagulation processes, J. Phys. A 14 (1981) 3389-3405.
18. P. Meakin, M.H. Ernst, Scaling in aggregation with breakup simulations and mean-field theory, Phys. Rev. Lett. 60 (1988) 2503-2506
19. Z.A. Melzak, A scalar transport equation, Trans. Amer. Math. Soc. 85 (1957) 547-560.
20. C.M. Sorensen, H.X. Zhang, T.W. Taylor, Cluster-size evolution in a coagulation-fragmentation system, Phys. Rev. Lett. 59 (1987) 363-366.
21. I.W. Stewart, A global existence theorem for the general coagulation-fragmentation equation with unbounded kernels, Math. Methods Appl. Sci. 11 (1989) 627-648.
22. I.W. Stewart, On the coagulation-fragmentation equation, Z. Angew. Math. Phys. 41 (1990) 917-924.
23. W.H. Stockmayer, Theory of molecular size distribution and gel formation in branched-chain polymers, J. Chem. Phys. 11 (1943) 45-55.
24. I.I. Vrabie, Compactness Methods for Nonlinear Evolutions, 2nd Edition, Pitman Monographs and Surveys in Pure and Applied Mathematics, Vol. 75, Longman, Harlow, 1995.
25. B. Wennberg, An example of nonuniqueness for solutions to the homogeneous Boltzmann equation, J. Statist. Phys. 95 (1999) 469-477.
26. R.M. Ziff, G. Stell, Kinetics of polymer gelation, J. Chem. Phys. 73 (1980) 3492-3499.