Sol-gel transition in a coagulation-diffusion model

Physica D: Nonlinear Phenomena

Volumn 141, Issue 3-4, 2000, Pages 221-247

  Herrero, M A ^a   Velazquez J J L ^a   Wrzosek, D ^b  

^a UNIVERSIDAD COMPLUTENSE DE MADRID   (Spain)

^b UNIVERSITY OF WARSAW   (Poland)

Author keywords

Cluster growth; Coagulation diffusion model; Sol gel transition

Indexed keywords

EID: 0001739620     PISSN: 01672789     EISSN: None     Source Type: Journal    
DOI: 10.1016/S0167-2789(00)00034-8     Document Type: Article

References (29)

1. M. Smoluchowski, Drei Vorträge über Diffusion, Brownische Bewegung und Koagulation von Kolloiden, Physik Z 17 (1916) 557-585.
2. S. Chandrasekhar, Stochastic problems in physics and astronomy, Rev. Mod. Phys. 15 (1) (1943) 1-91.
3. E.M. Hendriks, M.H. Ernst, R.M. Zoft, Coagulation equations with gelation, J. Stat. Phys. 31 (1983) 519-563.
4. G. Szell, R.M. Ziff, Kinetics of polymer gelation, J. Chem. Phys. 73 (1980) 3492-3499.
5. R.M. Ziff, Kinetics of polymerization, J. Stat. Phys. 23 (1980) 241-263.
6. R.L. Drake, A general mathematical survey of the coagulation equation, in: G.M. Hildy, J.R. Brok (Eds.), Topics in Current Aerosol Research, Part. 2, Pergamon Press, Oxford, 1972, pp. 203-237.
7. P.B. Dubovski, Mathematical Theory of Coagulation, Lecture Notes Series, Vol. 23, Seoul National University, 1994.
8. J.B. Mc Leod, On an infinite set of non-linear differential equations, Quart. J. Math. Oxford 2 (1962) 119-128.
9. R. Long, N.X. Xanh, Smoluchowski's theory of coagulation in colloids holds rigorously in the Boltzmann-Grad limit, Z. Wahrsch. verw. Gebiete 54 (1980) 227-280.
10. P.G.J. Van Dongen, Spatial fluctuations in reaction-limited aggregation, J. Stat. Phys. 54 (1989) 221-271.
11. M. Slemrod, Coagulation diffusion systems: derivation and existence of solutions for the diffuse interface structure equations, Physica D 46 (1990) 351-361.
12. F. Leyvraz, H.R. Tschudi, Singularities in the kinetics of coagulation processes, J. Phys. A 14 (1981) 3389-3405.
13. J.M. Ball, J. Carr, The discrete coagulation-fragmentation equations: existence, uniqueness and density conservation, J. Stat. Phys. 61 (1990) 203-234.
14. D. Wrzosek, Existence of solutions for the discrete coagulation-fragmentation model with diffusion, Topol. Meth. Nonlinear Anal. 9 (1997) 279-296.
15. P.J. Flory, Principles of Polymer Chemistry, Cornell Univ. Press, Ithaca, NY, USA, 1953.
16. F. Leyvraz, Existence and properties of post-gel solutions for the kinetic equations of coagulation, J. Phys. A 16 (1983) 2861-2873.
17. H. Jeon, Existence of gelling solutions for coagulation fragmentation equations, Commun. Math. Phys. 194 (1998) 541-567.
18. F.P. Costa, A finite dimensional dynamical model for gelation in coagulation processes, J. Nonlinear Sci. 8 (1998) 619-653.
19. Ph. Bénilan, D. Wrzosek, On an infinite system of reaction-diffusion equations, Adv. Math. Sci. Appl. 7 (1997) 351-366.
20. D. Gilbarg, N.S. Trudinger, Elliptic Partial Differential Equations of Second Order, Springer, Berlin, 1997.
21. L.C. Evans, Weak convergence methods for nonlinear partial differential equations, Am. Math. Soc. Regional Conference Series in Mathematics, Vol. 74, American Mathematical Society, Providence, RI, 1990.
22. M.A. Herrero, E. Medina, J.J.L. Velázquez, The birth of a cusp in the two-dimensional, undercooled Stefan problem, Quart. J. App. Math., in press.
23. M.A. Herrero, J.J.L. Velázquez, Blow-up behaviour of one-dimensional semilinear parabolic equations, Ann. Inst. Henri Poincaré 10 (2) (1993) 131-189.
24. M.A. Herrero, J.J.L. Velázquez, Blow-up profiles in one-dimensional semilinear parabolic problems, Commun. PDE 17 (1992) 205-219.
25. J.J.L. Velázquez, Higher-dimensional blow-up for semilinear parabolic equations, Commun. PDE 17 (1992) 1567-1596.
26. Ph. Laurençot, Global solutions to the discrete coagulation equations, submitted for publication.
27. V. Komornik, Exact Controllability and Stabilization, Masson, Paris, 1994.
28. P. Baras, J.C. Hassan, L. Veron, Compacité de l'operateur definissant la solution d'une equation d'evolution non homogène, C.R. Acad. Sci. Paris Ser. I 284 (1977) 799-802.
29. A. Pazy, Semigroups of Linear Operators and Applications to Partial Differential Equations, Springer, Berlin, 1983.