Global existence for the discrete diffusive coagulation-fragmentation equations in L1

Revista Matematica Iberoamericana

Volumn 18, Issue 3, 2002, Pages 731-745

  Laurençot, Philippe ^a   Mischler, Stéphane ^b  

^a INSTITUT DE MATHÉMATIQUES DE TOULOUSE   (France)

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

Author keywords

Breakage; Cluster growth; Coalescence; Existence; Infinite system of reaction diffusion equations; Weak compactness

Indexed keywords

EID: 0036996523     PISSN: 02132230     EISSN: 22350616     Source Type: Journal    
DOI: 10.4171/RMI/334     Document Type: Article

References (25)

1. AMANN, H.: Dual semigroups and second order linear elliptic boundary value problems. Israel J. Math. 45 (1983), 225-254.
2. AMANN, H.: Coagulation-fragmentation processes. Arch. Rational Mech. Anal. 151 (2000), 339-366.
3. BALL, J.M. AND CARR, J.: The discrete coagulation-fragmentation equations: existence, uniqueness, and density conservation. J. Statist. Phys. 61 (1990), 203-234.
4. BARAS, P.: Compacité de l'opérateur f → u solution d'une équation non linéaire (du/dt) + Au ∋ f. C. R. Acad. Sci. Paris Sér. I Math. 286 (1978), 1113-1116.
5. BARAS, P. HASSAN, J.C. AND VÉRON, L.: Compacité de l'opérateur définissant la solution d'une équation d'évolution non homogène. C. R. Acad. Sci. Paris Sér. I Math. 284 (1977), 799-802.
6. BÉNILAN, PH. AND WRZOSEK, D.: On a infinite system of reaction-diffusion equations. Adv. Math. Sci. Appl. 7 (1997), 349-364.
7. CHAE, D. AND DUBOVSKIǏ, P.B.: Existence and uniqueness for spatially inhomogeneous coagulation equation with sources and effluxes. Z. Angew. Math. Phys. 46 (1995), 580-594.
8. COLLET, J.F. AND POUPAUD, F.: Existence of solutions to coagulation-fragmentation systems with diffusion. Transport Theory Statist. Phys. 25 (1996), 503-513.
9. COSTA, F.P. DA: Existence and uniqueness of density conserving solutions to the coagulation-fragmentation equations with strong fragmentation. J. Math. Anal. Appl. 192 (1995), 892-914.
10. DRAKE, R.L.: A general mathematical survey of the coagulation equation, in Topics in Current Aerosol Research (part 2). International Reviews in Aerosol Physics and Chemistry, Pergamon Press, Oxford, 1972, 203-376.
11. GUIAŞ, F.: Convergence properties of a stochastic model for coagulation-fragmentation processes with diffusion. Stochastic Anal. Appl. 19 (2001), 245-278.
12. HERRERO, M.A., VELÁZQUEZ, J.J.L. AND WRZOSEK, D.: Sol-gel transition in a coagulation-diffusion model. Phys. D 141 (2000), 221-247.
13. JEON, I.: Existence of gelling solutions for coagulation-fragmentation equations. Comm. Math. Phys. 194 (1998), 541-567.
14. LAURENÇOT, PH. AND WRZOSEK, D.: Fragmentation-diffusion model. Existence of solutions and asymptotic behaviour. Proc. Roy. Soc. Edinburgh Sect. A 128 (1998), 759-774.
15. LAURENÇOT, PH. AND WRZOSEK, D.: The Becker-Döring model with diffusion. I. Basic properties of solutions. Colloq. Math. 75 (1998), 245-269.
16. MCGRADY, E.D. AND ZIFF, R.M.: "Shattering" transition in fragmentation. Phys. Rev. Lett. 58 (1987), 892-895.
17. PERELSON, A.S. AND SAMSEL, R.W.: Kinetics of red blood cell aggregation: an example of geometric polymerization, in Kinetics of Aggregation and Gelation. F. Family and D.P. Landau (eds.), Elsevier, 1984.
18. SAFRONOV, V.S.: Evolution of the Protoplanetary Cloud and Formation of the Earth and the Planets, Israel Program for Scientific Translations Ltd., Jerusalem, 1972.
19. SIMONS, S. AND SIMPSON, D.R.: The effect of particle coagulation on the diffusive relaxation of a spatially inhomogeneous aerosol. J. Phys. A 21 (1988), 3523-3536.
20. SLEMROD, M.: Coagulation-diffusion systems: derivation and existence of solutions for the diffuse interface structure equations. Phys. D 46 (1990), 351-366.
21. SMOLUCHOWSKI, M.: Drei Vorträge über Diffusion, Brownsche Molekularbewegung und Koagulation von Kolloidteilchen. Physik. Zeitschr. 17 (1916), 557-599.
22. SMOLUCHOWSKI, M.: Versuch einer mathematischen Theorie der Koagulationskinetik kolloider Lösungen. Zeitschrift f. physik. Chemie 92 (1917), 129-168.
23. SPOUGE, J.L.: An existence theorem for the discrete coagulation-fragmentation equations. Math. Proc. Cambridge Philos. Soc. 96 (1984), 351-357.
24. WRZOSEK, D.: Existence of solutions for the discrete coagulation-fragmentation model with diffusion. Topol. Methods Nonlinear Anal. 9 (1997), 279-296.
25. WRZOSEK, D.: Mass-conserving solutions to the discrete coagulation-fragmentation model with diffusion. Nonlinear Anal. 49 (2002), 297-314.