The Becker-Döring model with diffusion. I. Basic properties of solutions

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1. [1] H. Amann, Dual semigroups and second order linear elliptic boundary value problems, Israel J. Math. 45 (1983), 225-254. 
2. [2] J. M. Ball and J. Carr, The discrete coagulation-fragmentation equations: existence, uniqueness, and density conservation, J. Statist. Phys. 61 (1990), 203-234. Zbl1217.82050
3. [3] J. M. Ball and J. Carr, Asymptotic behaviour of solutions to the Becker-Döring equations for arbitrary initial data, Proc. Roy. Soc. Edinburgh Sect. A 108 (1988), 109-116. Zbl0656.58021
4. [4] J. M. Ball, J. Carr and O. Penrose, The Becker-Döring cluster equations: basic properties and asymptotic behaviour of solutions, Comm. Math. Phys. 104 (1986), 657-692. Zbl0594.58063
5. [5] P. Baras, J. C. Hassan et L. Véron, Compacité de l'opérateur définissant la solution d'une équation d'évolution non homogène, C. R. Acad. Sci. Paris Sér. I 284 (1977), 799-802. Zbl0348.47026
6. [6] P. Bénilan and D. Wrzosek, On an infinite system of reaction-diffusion equations, Adv. Math. Sci. Appl. 7 (1997), 349-364. 
7. [7] J. F. Collet and F. Poupaud, Existence of solutions to coagulation-fragmentation systems with diffusion, Transport. Theory Statist. Phys. 25 (1996), 503-513. Zbl0870.35117
8. [8] O. A. Ladyzhenskaya, V. A. Solonnikov and N. N. Uraltseva, Linear and Quasilinear Equations of Parabolic Type, Transl. Math. Monographs 23, Amer. Math. Soc., Providence, 1968. 
9. [9] Ph. Laurençot and D. Wrzosek, Fragmentation-diffusion model. Existence of solutions and asymptotic behaviour, Proc. Roy. Soc. Edinburgh Sect. A, to appear. Zbl0912.35031
10. [10] Ph. Laurençot and D. Wrzosek, The Becker-Döring model with diffusion. II. Long time behaviour, submitted. Zbl0913.35070
11. [11] R. H. Martin and M. Pierre, Nonlinear reaction-diffusion systems, in: Nonlinear Equations in Applied Science, W. F. Ames and C. Rogers (eds.), Academic Press, Boston, 1992. 
12. [12] O. Penrose and A. Buhagiar, Kinetics of nucleation in a lattice gas model: microscopic theory and simulation compared, J. Statist. Phys. 30 (1983), 219-241. 
13. [13] F. Rothe, Global Solutions of Reaction-Diffusion Systems, Lecture Notes in Math. 1072, Springer, Berlin, 1984. Zbl0546.35003
14. [14] M. Slemrod, Trend to equilibrium in the Becker-Döring cluster equations, Nonlinearity 2 (1989), 429-443. Zbl0709.60528
15. [15] J. L. Spouge, An existence theorem for the discrete coagulation-fragmentation equations, Math. Proc. Cambridge Philos. Soc. 96 (1984), 351-357. Zbl0541.92029
16. [16] D. Wrzosek, Existence of solutions for the discrete coagulation-fragmentation model with diffusion, Topol. Methods Nonlinear Anal. 9 (1997), 279-296. Zbl0892.35077
17. [17] A. Ziabicki, Generalized theory of nucleation kinetics. IV. Nucleation as diffusion in the space of cluster dimensions, positions, orientations and internal structure, J. Chem. Phys. 85 (1986), 3042-3056. 

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