On the application of substochastic semigroup theory to fragmentation models with mass loss

A linear integro-differential equation modelling multiple fragmentation with inherent mass loss is investigated by means of substochastic semigroup theory. The existence of a semigroup is established and, under natural conditions on certain coefficients, the generator of this semigroup is identified. This yields, in particular, a validation of the formal mass-loss rate equation for the model.  2003 Elsevier Inc. All rights reserved