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

Banasiak, Jacek and Lamb, Wilson (2003) On the application of substochastic semigroup theory to fragmentation models with mass loss. Journal of Mathematical Analysis and Applications, 284 (1). pp. 9-30. ISSN 0022-247X

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Abstract

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.