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An existence theorem for the discrete coagulation–fragmentation equations

II. Inclusion of source and efflux terms

Published online by Cambridge University Press:  24 October 2008

John L. Spouge
John L. Spouge
Affiliation:
Theoretical Biology and Biophysics, Los Alamos National Laboratory, Los Alamos, NM 86745, U.S.A.
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Abstract

This paper proves the existence of solutions for the discrete coagulation–fragmentation equation over all times, even when source and efflux terms are present. The hypotheses required cover most physical applications. Roughly speaking, the hypotheses ensure a finite flux of mass through the system. The techniques used, which extend those in I of this series, may apply to other infinite systems of differential equations.

Type
Research Article
Information
Mathematical Proceedings of the Cambridge Philosophical Society , Volume 98 , Issue 1 , July 1985 , pp. 183 - 185
Copyright
Copyright © Cambridge Philosophical Society 1985

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References

REFERENCES

[1]Hendriks, E. M. and Ziff, R. M.. Coagulation in a continuously stirred tank reactor(Preprint.)Google Scholar
[2]Klety, J. D.. A class of solutions to the steady-state, source enhanced kinetic coagulation equation. J. Atmos. Sci. 32 (1975), 380–389.2.0.CO;2>CrossRefGoogle Scholar
[3]Leyvraz, F.. Large-time behaviour of the Smoluchowski equations of coagulation. Phys. Rev. A 29 (1984), 854–857.CrossRefGoogle Scholar
[4]Leyvtaz, F. and Tschudi, H. R.. Singularities in the kinetics of coagulation processes. J. Phys. A: Math. Gen. 14 (1983), 3389–3405.CrossRefGoogle Scholar
[5]Lushnikov, A. and Piskunov, V.N.. Stationary coagulation in spatially nonhomogeneous systems situated in an homogeneous external force field. Dokl. Akad. Nauk. SSSR (Eng. tr.) (1976), 493–496.Google Scholar
[6]Spouge, J. L.. An existence theorem for the discrete coagulation-fragmentation equations. Math. Proc. Cambridge Philos. Soc. 96 (1984), 351–357.CrossRefGoogle Scholar