On the positivity of solutions to the Smoluchowski equations

• Author(s): Costa, Fernando Pestana da
• Date: 1995
• Persistent ID: http://hdl.handle.net/10400.2/1490
• Origin: Repositório Aberto da Universidade Aberta
• Subject(s): Smoluchowski coagulation equations; Positivity of solutions
• Document Type: Article
• Language: English

Description

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.