Spatially non-homogeneous coagulation equations with source terms
Authors:
M. Shirvani and H. J. van Roessel
Journal:
Quart. Appl. Math. 62 (2004), 651-670
MSC:
Primary 82C21; Secondary 34A12, 34A34
DOI:
https://doi.org/10.1090/qam/2104267
MathSciNet review:
MR2104267
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Abstract: The physical process of coagulation or coalescence of particles is often modelled by Smoluchowski’s coagulation equation, an infinite system of nonlinear differential equations governing the binary interactions of particles of different sizes. One of the physical assumptions underlying the coagulation equation is spatial homogeneity, in particular, the assumption that coagulation of particles is governed only by particle type or size. The physical shape of the cloud of particles, as well as the relative position of particles of various type, are ignored.
- F. R. Gantmacher, Matrizenrechnung. II. Spezielle Fragen und Anwendungen, Hochschulbücher für Mathematik, Bd. 37, VEB Deutscher Verlag der Wissenschaften, Berlin, 1959 (German). MR 0107647
M. Gimenez, M. Schlamp, and A. Clausse, Analysis of the spatial distribution of aerosol dispersions, Annals of Nuclear Energy 22, 17–28 (1995)
- Einar Hille, Ordinary differential equations in the complex domain, Dover Publications, Inc., Mineola, NY, 1997. Reprint of the 1976 original. MR 1452105
A. Kuciauskas, Tracking troposphoric aerosols across the Pacific Ocean, Naval Postgraduate School Report, 1999
M. H. Lee, On the validity of the coagulation equation and the nature of runaway growth, Icarus 143, 74–86 (2000)
- 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), no. 3, 526–535. MR 1166971, DOI https://doi.org/10.1007/BF00946244
- M. Shirvani and H. J. Van Roessel, Existence and uniqueness of solutions of Smoluchowski’s coagulation equation with source terms, Quart. Appl. Math. 60 (2002), no. 1, 183–194. MR 1878265, DOI https://doi.org/10.1090/qam/1878265
H. Wielandt, Topics in the Analytic Theory of Matrices, Department of Mathematics, University of Wisconsin-Madison, 1967
F. R. Gantmacher, The Theory of Matrices, Chelsea, 1959
M. Gimenez, M. Schlamp, and A. Clausse, Analysis of the spatial distribution of aerosol dispersions, Annals of Nuclear Energy 22, 17–28 (1995)
E. Hille, Ordinary Differential Equations In the Complex Domain, Dover, 1997
A. Kuciauskas, Tracking troposphoric aerosols across the Pacific Ocean, Naval Postgraduate School Report, 1999
M. H. Lee, On the validity of the coagulation equation and the nature of runaway growth, Icarus 143, 74–86 (2000)
M. Shirvani and H. J. Van Roessel, The mass-conserving solutions of Smoluchowski’s coagulation equation: The general bilinear kernel, Z. angew. Math. Phys. 43, 526–535 (1992)
M. Shirvani and H. J. Van Roessel, Existence and uniqueness of solutions of Smoluchowski’s coagulation equation with source terms, Quarterly of Applied Mathematics LX(1), 183–194 (2002)
H. Wielandt, Topics in the Analytic Theory of Matrices, Department of Mathematics, University of Wisconsin-Madison, 1967
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© Copyright 2004
American Mathematical Society
