The Discrete Agglomeration Model: Equivalent Problems
James L. Moseley
West Virginia University, Morgantown, USA.
DOI: 10.4236/am.2012.311236   PDF    HTML   XML   4,047 Downloads   6,302 Views   Citations

Abstract

In this paper we develop equivalent problems for the Discrete Agglomeration Model in the continuous context.

Share and Cite:

J. Moseley, "The Discrete Agglomeration Model: Equivalent Problems," Applied Mathematics, Vol. 3 No. 11, 2012, pp. 1702-1718. doi: 10.4236/am.2012.311236.

Conflicts of Interest

The authors declare no conflicts of interest.

References

[1] W. M. Goldberger, “Collection of Fly Ash in a Self-Agglomerating Fluidized Bed Coal Burner,” Proceedings of the ASME Annual Meeting, American Society of Mechanical Engineers, Pittsburg, 1967, 16 pp.
[2] J. H. Siegell, “Defluidization Phenomena in Fluidized Beds of Sticky Particles at High Temperatures,” Ph.D. Thesis, City University of New York, New York, 1976.
[3] R. L. Drake, “A General Mathematics Survey of the Coagulation Equation,” In: G. M. Hidy and J. R. Brock, Eds., Topics in Current Aerosol Research, Pergamon Press, New York, 1972.
[4] M. Von Smoluchowski, “Versuch Einer Mathematichen Theorie der Koagulationskinetik Kollider L?sungen,” Zeitschrift fuer Physikalische Chemie, Vol. 92, No. 2, 1917, pp. 129-168.
[5] H. Müller, “Zur Allgemeinen Theorie Ser Raschen Koagulation,” Kolloidchemische Beihefte, Vol. 27, No. 6-12, 1928, pp. 223-250.
[6] D. Morganstern, “Analytical Studies Related to the Maxwell-Boltzmann Equation,” Journal of Rational Mechanics and Analysis, Vol. 4, No. 5, 1955, pp. 533-555.
[7] Z. A. Melzack, “A Scalar Transport Equation,” Transactions of the American Mathematical Society, Vol. 85, No. 2, 1957, pp. 547-560. doi:10.1090/S0002-9947-1957-0087880-6
[8] J. B. McLeod, “On a Finite Set of Nonlinear Differential Equations (II),” Quarterly Journal of Mathematics, Vol. 13, No. 1, 1962, pp. 193-205. doi:10.1093/qmath/13.1.193
[9] A. Marcus, “Unpublished Notes,” Rand Corporation, Santa Monica, 1965.
[10] W. H. White, “A Global Existence Theorem for Smoluchowski’s Coagulation Equations,” Proceedings of the American Mathematical Society, Vol. 80, No. 2, 1980, pp. 273-276.
[11] J. L. Spouge, “An Existence Theorem for the Discrete Coagulation-Fragmentation Equations,” Mathematical Proceedings of the Cambridge Philosophical Society, Vol. 96, No. 2, 1984, pp. 351-357. doi:10.1017/S0305004100062253
[12] R. P. Treat, “An Exact Solution of the Discrete Smoluchowski Equation and Its Correspondence to the Solution in the Continuous Equation,” Journal of Physics A: Mathematical and General, Vol. 23, No. 13, 1990, pp. 3003-3016. doi:10.1088/0305-4470/23/13/035
[13] D. J. McLaughlin, W. Lamb and A. C. McBride, “An Existence and Uniqueness Result for a Coagulation and Multi-Fragmentation Equation,” SIAM Journal on Mathematical Analysis, Vol. 28, No. 5, 1997, pp 1173-1190. doi:10.1137/S0036141095291713
[14] J. L. Moseley, “The Discrete Agglomeration Model with Time Varying Kernel,” Nonlinear Analysis: Real World Applications, Vol. 8, No. 2, 2007, pp. 405-423. doi:10.1016/j.nonrwa.2005.12.001
[15] J. L. Moseley, “The Discrete Agglomeration Model: The Fundamental Agglomeration Problem with a Time-Varying Kernel,” Far East Journal of Applied Mathematics, Vol. 47, No. 1, 2010, pp. 17-34.
[16] R. H. Martin, “Nonlinear Operators and Differential Equations in Banach Spaces,” John Wiley & Sons, New York, 1976
[17] A.W. Naylor and G. R. Sell, “Linear Operator Theory in Engineering and Science,” Holt Rinehart ND Winston, Inc., New York, 1971.
[18] R. G. Bartle, “The Elements of Real Analysis,” John Wiley & Sons, New York, 1976.
[19] J. Stewart, “Essential Calculus, Early Transcendentals,” Thomson Brooks/Cole, Independence, 2007
[20] F. Brauer and J. A. Nohel, “The Qualitative Theory of Ordinary Differential Equations,” W. A. Benjamin, Inc., New York, 1969
[21] W. Kaplan, “Advanced Calculus,” Addison-Wesley Publishing Company, Redwood City, 1991.

Copyright © 2024 by authors and Scientific Research Publishing Inc.

Creative Commons License

This work and the related PDF file are licensed under a Creative Commons Attribution 4.0 International License.