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On the positivity of solutions to the Smoluchowski equations
Author(s) -
Costa F. P. Da
Publication year - 1995
Publication title -
mathematika
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.955
H-Index - 29
eISSN - 2041-7942
pISSN - 0025-5793
DOI - 10.1112/s0025579300014686
Subject(s) - mathematics , smoluchowski coagulation equation , mathematical analysis , pure mathematics , statistical physics , physics
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.peerreviewe