AM  Vol.3 No.11 , November 2012
The Discrete Agglomeration Model: Equivalent Problems
Abstract: In this paper we develop equivalent problems for the Discrete Agglomeration Model in the continuous context.
Cite this paper: J. Moseley, "The Discrete Agglomeration Model: Equivalent Problems," Applied Mathematics, Vol. 3 No. 11, 2012, pp. 1702-1718. doi: 10.4236/am.2012.311236.

[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[9]   A. Marcus, “Unpublished Notes,” Rand Corporation, Santa Monica, 1965.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.