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Centred on the vision of 'Delivering Total Engineering', DMEM is a centre for excellence in the processes, systems and technologies needed to support and enable engineering from concept to remanufacture. From user-centred design to sustainable design, from manufacturing operations to remanufacturing, from advanced materials research to systems engineering.

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The discrete fragmentation equations : semigroups, compactness and asynchronous exponential growth

Banasiak, Jacek and Lamb, Wilson (2012) The discrete fragmentation equations : semigroups, compactness and asynchronous exponential growth. Kinetic and Related Models, 5 (2). pp. 223-236. ISSN 1937-5093

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Abstract

In this paper we present a class of fragmentation semigroups which are compact in a scale of spaces defined in terms of finite higher moments. We use this compactness result to analyse the long time behaviour of such semigroups and, in particular, to prove that they have the asynchronous growth property. We note that, despite compactness, this growth property is not automatic as the fragmentation semigroups are not irreducible.