A continuum individual based model of fragmentation: dynamics of correlation functions

Tanaś, Agnieszka

Annales Universitatis Mariae Curie-Skłodowska. Mathematica , Tome 69 (2015) no. 2.

Résumé

An individual-based model of an infinite system of point particles in Rd is proposed and studied. In this model, each particle at random produces a finite number of new particles and disappears afterwards. The phase space for this model is the set Γ of all locally finite subsets of Rd. The system's states are probability measures on  Γ the Markov evolution of which is described in terms of their  correlation functions in a scale of Banach spaces. The existence and uniqueness of solutions of the corresponding evolution equation are proved.

Détail

Keywords: Configuration space, individual-based model, birth-and-death process, correlation function, scale of Banach spaces, Ovcyannikov method.

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