Weak solutions to the Cauchy problem for the diffusive discrete coagulation-fragmentation system

Journal of Mathematical Analysis and Applications

Volumn 289, Issue 2, 2004, Pages 405-418

  Wrzosek, Dariusz ^a  

^a UNIVERSITY OF WARSAW   (Poland)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 1642519787     PISSN: 0022247X     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.jmaa.2003.08.022     Document Type: Article

References (32)

1. 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.
2. H. Amann, Coagulation-fragmentation processes, Arch. Rational Mech. Anal. 151 (2000) 339-366.
3. J.M. Ball, J. Carr, The discrete coagulation-fragmentation equations: existence, uniqueness, and density conservation, J. Statist. Phys. 61 (1990) 203-234.
4. Ph. Bénilan, D. Wrzosek, On a infinite system of reaction-diffusion equations, Adv. Math. Sci. Appl. 7 (1997) 349-364.
5. J.F. Collet, F. Poupaud, Existence of solutions to coagulation-fragmentation systems with diffusion, Transport Theory Statist. Phys. 25 (1996) 503-513.
6. M. Deaconu, N. Fournier, Probabilistic approach of some discrete and continuous coagulation equations with diffusion, Stochastic Process. Appl. 101 (2002) 83-111.
7. P.G.J. van Dongen, Spatial fluctuations in reaction-limited aggregation, J. Statist. Phys. 54 (1989) 221-271.
8. R.L. Drake, A general mathematical survey of the coagulation equation, in: Topics in Current Aerosol Research (Part 2), International Reviews in Aerosol Physics and Chemistry, Pergamon, 1972, pp. 203-376.
9. R.E. Edwards, Functional Analysis: Theory and Applications, Holt, Rinehart, Winston, 1965.
10. M. Escobedo, S. Mischler, B. Perthame, Gelation in coagulation and fragmentation models, Comm. Math. Phys. 231 (2002) 157-188.
11. R Guiaş, Coagulation-fragmentation processes: relations between finite particles models and differential equations, Preprint SFB 359, Ph.D. thesis, Universität Heidelberg, 1998.
12. E.M. Hendriks, M.H. Ernst, R.M. Ziff, Coagulation equations with gelation, J. Statist. Phys. 31 (1983) 519-563.
13. M.A. Herrero, J.J.L. Velázquez, D. Wrzosek, Sol-gel transition in a coagulation-diffusion model, Phys. D 141 (2000) 221-247.
14. I. Jeon, Existence of gelling solutions for coagulation-fragmentation equations, Comm. Math. Phys. 194 (1998) 541-567.
15. M. Lachowicz, D. Wrzosek, A nonlocal coagulation-fragmentation model, Appl. Math. (Warsaw) 27 (2000) 45-66.
16. R. Lang, Nguyen Xuan Xanh, Smoluchowski's theory of coagulation in colloids holds rigorously in the Boltzmann-Grad-limit, Z. Wahrscheinlichkeitstheorie Verw. Gebiete 54 (1980) 227-280.
17. 1, Rev. Mat. Iberoamericana 18 (2002) 731-745.
18. Ph. Laurençot, S. Mischler, The continuous coagulation-fragmentation equations with diffusion, Arch. Rational Mech. Anal. 162 (2002) 45-99.
19. Ph. Laurençot, D. Wrzosek, The Becker-Döring model with diffusion. I. Basic properties of solutions, Colloq. Math. 75 (1998) 245-269.
20. Ph. Laurençot, D. Wrzosek, Discrete coagulation-fragmentation models, in: Activity Report 1995-1999, Milan Research Center for Industrial and Applied Mathematics, Department of Mathematics, Università degli Studi di Milano, 1999.
21. F. Leyvraz, H.R. Tschudi, Singularities in the kinetics of coagulation processes, J. Phys. A 14 (1981) 3389-3405.
22. A.S. Perelson, R.W. Samsel, Kinetics of red blood cell aggregation: an example of geometric polymerization, in: F. Family, D.P. Landau (Eds.), Kinetics of Aggregation and Gelation, Elsevier, 1984, pp. 137-144.
23. V.S. Safronov, Evolution of the Protoplanetary Cloud and Formation of the Earth and the Planets, Israel Program for Scientific Translations, 1972.
24. J.H. Seinfeld, Atmospheric Chemistry and Physics of Air Pollution, Wiley, New York, 1986.
25. S. Simons, D.R. Simpson, The effect of particle coagulation on the diffusive relaxation of a spatially inhomogeneous aerosol, J. Phys. A 21 (1988) 3523-3536.
26. M. Slemrod, Coagulation-diffusion systems: derivation and existence of solutions for the diffuse interface structure equations, Phys. D 46 (1990) 351-366.
27. M. Smoluchowski, Drei Vorträge über Diffusion, Brownsche Molekularbewegung und Koagulation von Kolloidteilchen, Phys. Z. 17 (1916) 557-599.
28. M. Smoluchowski, Versuch einer mathematischen Theorie der Koagulationskinetik kolloider Lösungen, Z. Phys. Chemie 92 (1917) 129-168.
29. I.I. Vrabie, Compactness Methods for Nonlinear Evolutions, 2nd ed., in: Pitman Monogr. Surveys Pure Appl. Math., Vol. 75, Longman, Harlow, 1995.
30. D. Wrzosek, Existence of solutions for the discrete coagulation-fragmentation model with diffusion, Topol. Methods Nonlinear Anal. 9 (1997) 279-296.
31. D. Wrzosek, Mass-conserving solutions to the discrete coagulation-fragmentation model with diffusion, Nonlinear Anal. 49 (2002) 297-314.
32. R.M. Ziff, Kinetics of polymerization, J. Statist. Phys. 23 (1980) 241-263.