Fragmentation-diffusion model. Existence of solutions and their asymptotic behaviour

Royal Society of Edinburgh - Proceedings A

Volumn 128, Issue 4, 1998, Pages 759-774

  Laurençot, Philippe ^a   Wrzosek, Dariusz ^b  

^a UNIVERSITÉ HENRI POINCARÉ NANCY 1   (France)

^b UNIVERSITY OF WARSAW   (Poland)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 3042612930     PISSN: 03082105     EISSN: None     Source Type: Journal    
DOI: 10.1017/S0308210500021764     Document Type: Article

References (19)

1. H. Amann. Dual semigroups and second order linear elliptic boundary value problems. Israel J. Math. 45 (1983), 225-54.
2. J. M. Ball and J. Carr. The discrete coagulation-fragmentation equations: existence, uniqueness, and density conservation. J. Statist. Phys. 61 (1990), 203-34.
3. P. Baras. Compacité de l'opérateur f → u solution d'une équation non linéaire (du/dt) + Au ∋ f. C. R. Acad. Sci. Paris, Sér. A 286 (1978), 1113-16.
4. Ph. Bénilan and D. Wrzosek. On an infinite system of reaction-diffusion equations. Adv. Math. Sci. Appl. 7 (1997), 349-64.
5. J. Carr. Asymptotic behaviour of solutions to the coagulation-fragmentation equations. I. The strong fragmentation case. Proc. Roy. Soc. Edinburgh Sect. A 121 (1992), 231-44.
6. J. Carr and F. P. da Costa. Asymptotic behaviour of solutions to the coagulation-fragmentation equations. II. Weak fragmentation. J. Statist. Phys. 77 (1994), 89-123.
7. J. F. Collet and F. Poupaud. Existence of solutions to coagulation-fragmentation systems with diffusion. Transport Theory Statist. Phys. 25 (1996), 503-13.
8. J. F. Collet and F. Poupaud. Asymptotic behaviour of solutions to the diffusive coagulation-fragmentation system. Phys. D. 114 (1998), 123-46.
9. P. Deuflhard and M. Wulkow. Towards an efficient computational treatment of heterogeneous polymer reactions. In Computational Ordinary Differential Equations, ed. S. O. Fatuula, 287-306 (Paris: University of Paris, 1992).
10. P. G. J. van Dongen. Spatial fluctuations in reaction-limited aggregation. J. Statist. Phys. 54 (1989), 221-71.
11. R. Drake. In Topics in Current Aerosol Research, eds. G. M. Hidy and J. R. Brock, A general mathematical survey of the coagulation equation, 202-376. (Oxford, Pergamon Press, 1972).
12. E. M. Hendriks, M. H. Ernst and R. M. Ziff. Coagulation equations with gelation. J. Statist. Phys. 31 (1983), 519-63.
13. R. H. Martin and M. Pierre. Nonlinear reaction-diffusion systems. In Nonlinear Equations in Applied Science, eds. W. F. Ames and C. Rogers, (Boston: Academic Press, 1992).
14. A. Pazy. Semigroups of Linear Operators and Applications to Partial Differential Equations (New York: Springer, 1983).
15. M. Slemrod. Coagulation-diffusion systems: derivation and existence of solutions for the diffuse interface structure equations. Phys. D 46 (1990), 351-66.
16. M. Smoluchowski. Versuch einer mathematischen Theorie der kolloiden Lösungen. Z. Phys. Chem. 92 (1917), 129-68.
17. D. Wrzosek. Existence of solutions for the discrete coagulation-fragmentation model with diffusion. Topol. Methods Nonlinear Anal. (to appear).
18. R. M. Ziff. Kinetics of polymerization. J. Statist. Phys. 23 (1980), 241-63.
19. R. M. Ziff and E. D. McGrady. The kinetics of cluster fragmentation and depolymerisation. J. Phys. A 18 (1985), 3027-37.