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A global existence theorem for Smoluchowski's coagulation equations


Author: Warren H. White
Journal: Proc. Amer. Math. Soc. 80 (1980), 273-276
MSC: Primary 34A45; Secondary 34G20, 80A30
DOI: https://doi.org/10.1090/S0002-9939-1980-0577758-1
MathSciNet review: 577758
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Abstract: A countable system of nonlinear ordinary differential equations is shown to admit solutions valid over all positive time.


References [Enhancements On Off] (What's this?)

  • [1] M. v. Smoluchowski, Versuch einer mathematischen Theorie der koagulationskinetik kolloider Losungen, Z. Phys. Chem. 92 (1918), 129-168.
  • [2] R. L. Drake, A general mathematical survey of the coagulation equation, Topics in Current Aerosol Research 3 (Part 2), G. M. Hidy and J. R. Brock (eds.), Pergamon, Oxford, 1972, pp. 201-376.
  • [3] H. R. Pruppacher and J. D. Klett, Microphysics of clouds and precipitation, Reidel, Dordrecht, 1978.
  • [4] J. B. McLeod, On an infinite set of non-linear differential equations, Quart. J. Math. Oxford Ser. (2) 13 (1962), 119–128. MR 0139822, https://doi.org/10.1093/qmath/13.1.119
  • [5] J. B. McLeod, On an infinite set of non-linear differential equations. II, Quart. J. Math. Oxford Ser. (2) 13 (1962), 193–205. MR 0140745, https://doi.org/10.1093/qmath/13.1.193

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Additional Information

DOI: https://doi.org/10.1090/S0002-9939-1980-0577758-1
Article copyright: © Copyright 1980 American Mathematical Society