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On the positivity of solutions to the Smoluchowski equations

Part of: General theory in ordinary differential equations

Published online by Cambridge University Press:  26 February 2010

F. P. Da Costa
F. P. Da Costa
Affiliation:
Departamento de Matemática, Instituto Superior Tecnico, Av. Rovisco Pais, P-1096 Lisboa, Portugal.
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Extract

The dynamics of cluster growth can be modelled by the following infinite system of ordinary differential equations, first proposed by Smoluchowski, [8],

where cj=cj(t) represents the physical concentration of j-clusters (aggregates of j identical particles), aj,k=aj,k≥0 are the time-independent coagulation coefficients, measuring the effectiveness of the coagulation process between a j-cluster and a k-cluster, and the first sum in the right-hand side of (1) is defined to be zero if j = 1.

MSC classification

Secondary: 34A34: Nonlinear equations and systems, general
Type
Research Article
Information
Mathematika , Volume 42 , Issue 2 , December 1995 , pp. 406 - 412
Copyright
Copyright © University College London 1995

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References

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