On the dynamic scaling behaviour of solutions to the discrete smoluchowski equations

Proceedings of the Edinburgh Mathematical Society

Volumn 39, Issue 3, 1996, Pages 547-559

  Costa, F P D A ^a  

^a INSTITUTO SUPERIOR TÉCNICO   (Portugal)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 21444436970     PISSN: 00130915     EISSN: None     Source Type: Journal    
DOI: 10.1017/s0013091500023294     Document Type: Article

References (15)

1. J. M. BALL and J. CARR, The discrete coagulation-fragmentation equations: existence, uniqueness, and density conservation, J. Statist. Phys. 61 (1990), 203-234.
2. 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.
3. J. M. BALL, P. J. HOLMES, R. D. JAMES, R. L. PEGO and P. J. SWART, On the dynamics of fine structure, J. Nonlinear Sci. 1 (1991), 17-70.
4. J. CARR and F. P. DA COSTA, Instantaneous gelation in coagulation dynamics, Z. Angew. Math. Phys. 43 (1992), 974-983.
5. J. CARR and F. P. DA COSTA, Asymptotic behavior of solutions to the coagulation-fragmentation equations. II. Weak fragmentation, J. Statist. Phys. 77 (1994), 89-123.
6. F. P. DA COSTA, On the positivity of solutions to the Smoluchowski equations, Mathematika 42 (1995), 406-412.
7. R. DRAKE, A general mathematical survey of the coagulation equation, in G. M. Hidy and J. R. Brock (eds.), Topics in Current Aerosol Research (part 2) (International Reviews in Aerosol Physics and Chemistry, Pergamon Press, Oxford, 1972).
8. M. H. ERNST and P. G. VAN DONGEN, Scaling solutions of Smoluchowski's coagulation equations, J. Statist. Phys. 50 (1988), 295-329.
9. F. FAMILY and T. VICSEK, Dynamic scaling for aggregation of clusters, Phys. Rev. Lett. 52 (1984), 1669-1672.
10. S. FRIEDLANDER and C. WANG, The self-preserving particle size distribution for coagulation by brownian motion, J. Coll. Interface Sci. 22 (1966), 126-132.
11. L. K. HUA, Introduction to Number Theory (Springer-Verlag, Berlin, 1982).
12. M. KREER and O. PENROSE, Proof of dynamic scaling in Smoluchowski's coagulation equation with constant kernels, J. Statist. Phys. 74 (1994), 389-407.
13. M. SHIRVANI and H. VAN ROESSEL, The mass-conserving solutions of Smoluchowski's coagulation equation: the general bilinear kernel, Z. Angew. Math. Phys. 43 (1992), 526-535.
14. M. SLEMROD, Trend to equilibrium in the Becker-Döring cluster equations, Nonlinearity 2 (1989), 429-443.
15. W. WHITE, A global existence theorem for Smoluchowski's coagulation equation, Proc. Amer. Math. Soc. 80 (1980), 273-276.