The Redner - Ben-Avraham - Kahng cluster system

Costa, Fernando Pestana da; Pinto, João Teixeira; Sasportes, Rafael

http://hdl.handle.net/10400.2/2620

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Authors

Costa, Fernando Pestana da

Pinto, João Teixeira

Sasportes, Rafael

Abstract(s)

We consider a coagulation model first introduced by Redner, Ben-Avraham and Kahng in [11], the main feature of which is that the reaction between a j-cluster and a k-cluster results in the creation of a |j − k|-cluster, and not, as in Smoluchowski’s model, of a (j + k)-cluster. In this paper we prove existence and uniqueness of solutions under reasonably general conditions on the coagulation coefficients, and we also establish differenciability properties and continuous dependence of solutions. Some interesting invariance properties are also proved. Finally, we study the long-time behaviour of solutions, and also present a preliminary analysis of their scaling behaviour.

Keywords

Dynamics of ODEs Coagulation processes

URI

http://hdl.handle.net/10400.2/2620

Citation

Costa, Fernando Pestana da; Pinto, João Teixeira; Sasportes, Rafael - The Redner - Ben-Avraham - Kahng cluster system. "São Paulo Journal of Mathematical Sciences" [Em linha]. ISSN 1982-6907. Vol 6, nº 2 (2012), p. 171-201