Conservativeness in nonlocal fragmentation models

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Abstract

A nonlocal multiple fragmentation process, where fragmentation rate is size and position dependent, and new particles are distributed randomly in space, is investigated by means of substochastic semigroup theory. The main aim of the paper is to find conditions ensuring honesty of the process (nonshattering fragmentation). We provide an example showing that dishonesty also may be caused by spatial properties of the fragmentation rate.

Keywords

Fragmentation
Substochastic semigroup
Conservativeness

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